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Physics is about understanding what’s around us, from the smallest particle to the far reaches of the universe. Physicists are problem solvers, future shapers, and at Northumbria we empower our Physics students to think creatively about how to tackle the challenges we put in front of them.

The Physics MPhys offers motivated, industrious students an integrated Masters award, meaning that you gain a deeper understanding of Physics as a subject and tackle open research questions in Physics, achieving a higher qualification than many other graduates in the same job market.

Research strengths in areas such as quantum devices, smart and nano materials, soft matter, chaos theory and dynamical systems underpin our integrated Masters Physics course.

You will learn from world-leading experts, and develop transferable skills including problem solving, data analysis, computer programming, communication and research skills.

Northumbria has recently invested more than one million pounds into Physics facilities and learning environments, further enhancing our reputation for innovation and excellence. 

IOP logoRecognition

Recognised by the Institute of Physics (IOP) for the purpose of eligibility for Associate Membership.

 

95% of students agreed that staff are good at explaining things and 91% of students say that they are satisfied overall with their course (Unistats, 2016)

Physics is about understanding what’s around us, from the smallest particle to the far reaches of the universe. Physicists are problem solvers, future shapers, and at Northumbria we empower our Physics students to think creatively about how to tackle the challenges we put in front of them.

The Physics MPhys offers motivated, industrious students an integrated Masters award, meaning that you gain a deeper understanding of Physics as a subject and tackle open research questions in Physics, achieving a higher qualification than many other graduates in the same job market.

Research strengths in areas such as quantum devices, smart and nano materials, soft matter, chaos theory and dynamical systems underpin our integrated Masters Physics course.

You will learn from world-leading experts, and develop transferable skills including problem solving, data analysis, computer programming, communication and research skills.

Northumbria has recently invested more than one million pounds into Physics facilities and learning environments, further enhancing our reputation for innovation and excellence. 

IOP logoRecognition

Recognised by the Institute of Physics (IOP) for the purpose of eligibility for Associate Membership.

 

95% of students agreed that staff are good at explaining things and 91% of students say that they are satisfied overall with their course (Unistats, 2016)

Course Information

UCAS Code
F301

Level of Study
Undergraduate

Mode of Study
4 years full-time or 5 years with a placement (sandwich)/study abroad

Department
Mathematics, Physics and Electrical Engineering

Location
Ellison Building, Newcastle City Campus

City
Newcastle

Start
September 2019

Department / Mathematics, Physics and Electrical Engineering

Book an Open Day / Experience Physics MPhys (Hons)

Visit an Open Day to get an insight into what it's like to study Physics. Speak to staff and students from the course and get a tour of the facilities.

Physics students at Northumbria are taught through a wide range of methods, including directed learning, laboratory experiments and self-directed research. There is a strong emphasis on problem solving, ranging from laboratory sessions and seminars to develop solutions to ideal problems, to applying computational techniques to multi-variable constrained problems.

You will be exposed to and encouraged to use the latest technology, through dedicated facilities, to study and understand complex physical concepts.

Our assessment philosophy is to provide students with the opportunity to demonstrate their knowledge, understanding and application in a variety of ways and settings including laboratory experiments, presentations, assignments, exams, reports and project work.

Assessments will develop your communication skills while also testing your grasp of the learning outcomes for each module.

During your fourth year, we will introduce you to advanced and topical problems in Physics. Through the Research Physics Project, you will apply specialist knowledge and skills to tackle an open-ended research project.

Book an Open Day / Experience Physics MPhys (Hons)

Visit an Open Day to get an insight into what it's like to study Physics. Speak to staff and students from the course and get a tour of the facilities.

With a large number of staff linked to our MPhys (Hons) Physics course, each with their own specialist areas of interest, you will learn from some truly world-leading experts. Within a field as diverse as Physics, you will be exposed to an inspiring array of innovative thinkers working on cutting edge research into the biggest challenges humanity faces.

Whether you are interested in in quantum physics or soft and biological matter, our staff are not only teaching their specialist subjects but also writing textbooks and adding new knowledge and perspectives to our understanding of the world around us.

Our students rate us highly, with 90% expressing satisfaction with the course.

Staff / Meet the Team

We are an enthusiastic, committed, knowledgeable and likeable staff team, who are here to motivate you and propel you through your degree and beyond.

Book an Open Day / Experience Physics MPhys (Hons)

Visit an Open Day to get an insight into what it's like to study Physics. Speak to staff and students from the course and get a tour of the facilities.

Northumbria has recently invested more than one million pounds into Physics facilities, meaning our students have access to the state-of-the-art learning environments.

The Smart Materials and Surfaces Lab supports research into many specialist fields including super-water repellent surfaces and microfluidics. The Microwave Technology Lab is at the centre of exciting research into breast cancer detection and security screening for concealed weapons. The New and Renewable Energy Lab is closely connected to future-changing research into wind power, photovoltaics and electric vehicle battery testing.

Technology Enhanced Learning is core to the Physics course. You will undertake online tests and self-guided exercises, which have a positive impact on your formation as they enable you to work independently and to develop innovative thinking. 

Physics Facilities

The department of Mathematics, Physics and Electrical Engineering has modern laboratory and computing resources for learning, teaching, research, innovation and business engagement.

Virtual Tour

Come and explore our outstanding facilities in this interactive virtual tour.

University Library

At the heart of each Northumbria campus, our libraries provide a range of study space and technology to suit every learning style.

Book an Open Day / Experience Physics MPhys (Hons)

Visit an Open Day to get an insight into what it's like to study Physics. Speak to staff and students from the course and get a tour of the facilities.

At Northumbria your learning will be enhanced through one-to-one contact with the Physics department staff.  Key research interests of staff include:

  • Condensed matter, including quantum dots, photovoltaics and high-speed LEDs
  • Soft and biological matter, including smart materials, surfaces and biofluids
  • Power systems, including synchronous generators, wind energy conversion systems and induction machines
  • Mechanical systems including control of flexible joint and rigid robots
  • Communications systems including compressive sensing and chaotic synchronisation

Research in Physics is fundamental to the distinctive learning experience at Northumbria. Research at the frontiers of physics is often used to inform lectures and seminars, through simulations and reports on recent scientific enquiry. During your final year Physics Research Project, you get the opportunity to closely work with one of our world-leading research groups in areas such as quantum devices, smart materials, theoretical physics, optics, non-linear phenomena, etc.

Physics research in Northumbria is at the top-35 with 79% of our publications ranked world leading or internationally excellent by the Research Excellence Framework 2014.

Research / Mathematics, Physics and Electrical Engineering

From statistics to complex and nonlinear phenomena, astrophysics to smart materials, and communications to renewable energy, the pioneering research in the Department of Mathematics, Physics and Electrical Engineering focuses on a wide range of issues.

Book an Open Day / Experience Physics MPhys (Hons)

Visit an Open Day to get an insight into what it's like to study Physics. Speak to staff and students from the course and get a tour of the facilities.

According to research from the Institute of Physics (IOP), physics graduates earn £3,000 per year more than graduates from other subjects.

A Physics MPhys makes you highly employable in a range of sectors that value the core principles of problem solving and an analytical approach. The strong research focus at Northumbria enhances these skills, allowing you to develop the key subject specialism which can help you stand out from the crowd.

Laboratory-based modules will equip you with practical and computational skills that can be applied to a wide variety of problems and challenges. By your third year, you will be working on modules closely aligned with live departmental research. Our close links with electrical engineering courses and research also offers a significant advantage to our students as it broadens the range of industrial placement opportunities.

Physicists are currently in high demand, and throughout this Integrated Masters course you will develop valuable skills that can be applied to almost any problem. This opens up a wide range of careers across many sectors including research and development, and in a wide variety of areas such as medical imaging, consumer electronics and energy. 

Student Life

A great social scene can be found at the heart of our campuses, featuring award-winning bars and a huge range of clubs and societies to join you'll be sure to meet people who share your enthusiasms.

Book an Open Day / Experience Physics MPhys (Hons)

Visit an Open Day to get an insight into what it's like to study Physics. Speak to staff and students from the course and get a tour of the facilities.

From the first day of your Physics MPhys to the last, you will be empowered to take responsibility for and develop your own learning.  This experience will equip you with a valuable range of transferable skills from the analytical to the practical and interpersonal.

Our industry partners tell us they value highly the analytical skills of Northumbria Physics students such as estimation, quantitative modelling and statistical analysis, and these skills can be deployed across a wide range of disciplines in addition to research, such as healthcare to energy, electronics and finance.

Whatever you decide to do, you will have a strong employability potential as a result of having acquired the characteristics of a Northumbria graduate. These include the ability to think creatively while at the same time applying rigorous structure to solve complex problems. The integration of a Masters award will provide additional weight to your profile, and a crucial edge at the beginning of your career as a Physicist.

Book an Open Day / Experience Physics MPhys (Hons)

Visit an Open Day to get an insight into what it's like to study Physics. Speak to staff and students from the course and get a tour of the facilities.

Course in brief

Your course in brief

Year 1

Year one Introduces key ideas in physics such as the Standard Model of particle physics, and strengthens your mathematics skills.

Year 2

Year two Focuses on core physics subjects including quantum mechanics, special relativity and electromagnetism. In addition to a deep exploration of these topics, you will also enhance your understanding of advanced mathematics.

Year 3

Year three Optional placement year in industry. This year is an excellent opportunity to gain something extra for your CV, the real-world application and development of your skills and knowledge from industry experience.

Year 4

Year four Involves classes based on our research strengths such as quantum devices and control theory. You can tailor your degree in this year, for example by choosing to make it more theoretical or experimental.

Year 5

Year five Is centred on advanced physics and mathematics. These are explored through a Special Topics module and you will also perform a significant piece of independent research as a member of one of our research groups.

Who would this Course suit?

Do you want to discover something about the Universe that no one knew about before? If you also want a head start in your career, the integrated Masters degree in Physics from Northumbria University is a smart choice.

Entry Requirements 2019/20

Standard Entry

GCSE requirements:

A good GCSE profile is expected including Maths and English Language at minimum grade C or equivalent.  If you have studied for a new GCSE for which you will be awarded a numerical grade then you will need to achieve a minimum grade 4.

UCAS Tariff Points:

120-128 UCAS Tariff points including one or more of the following: 

GCE and VCE Advanced Level: 

From at least 2 GCE/VCE A Levels including Grade B in Mathematics and Physics

Edexcel/BTEC National Extended Diploma:

Distinction, Distinction, Merit in Engineering

Scottish Highers:

BBBCC - BBBBC at Higher level, CCC - BCC at Advanced Higher in Mathematics and Physics

Irish Highers:

BBBBB  - ABBBB including Mathematics and Physics

IB Diploma:

120-128 UCAS Tariff points including minimum score of 4 in at least three subjects at Higher level including Mathematics and Physics

Access to HE Diploma:

Award of full Access to HE Diploma in Engineering including 18 units at Distinction and 27 at Merit

Qualification combinations:

The University welcomes applications from students studying qualifications from different qualification types - for example A level and a BTEC qualification in combination, and if you are made an offer you will be asked to achieve UCAS Tariff points from all of the qualifications you are studying at level 3.  Should the course you wish to study have a subject specific requirement then you must also meet this requirement, usually from GCE A level.

Plus one of the following:

  • International/English Language Requirements:

    Applicants from the EU:

    Applicants from the EU are welcome to apply and if the qualification you are studying is not listed here then please contact the Admissions Team for advice or see our EU Applicants pages here https://www.northumbria.ac.uk/international/european-union/eu-applications/

    International Qualifications:

    If you have studied a non UK qualification, you can see how your qualifications compare to the standard entry criteria, by selecting the country that you received the qualification in, from our country pages. Visit www.northumbria.ac.uk/yourcountry

    English Language Requirements:

    International applicants are required to have a minimum overall IELTS (Academic) score of 6.0 with 5.5 in each component (or approved equivalent*).

    *The university accepts a large number of UK and International Qualifications in place of IELTS. You can find details of acceptable tests and the required grades you will need in our English Language section. Visit www.northumbria.ac.uk/englishqualifications"

Fees and Funding 2019/20 Entry

UK/EU Fee in Year 1**: £9,250

International Fee in Year 1: £15,000

ADDITIONAL COSTS

There are no Additional Costs

FUNDING INFORMATION

Click here for UK and EU undergraduate funding and scholarships information.

Click here for International undergraduate funding and scholarships information.

Click here for UK/EU undergraduate tuition fee information**.

Click here for International undergraduate tuition fee information.

Click here for additional costs which may be involved while studying.

Click here for information on fee liability.

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* By submitting your information you are consenting to your data being processed by Northumbria University (as Data Controller) and Campus Management Corp. (acting as Data Processor). To see the University's privacy policy please click here

Modules Overview

Modules

Module information is indicative and is reviewed annually therefore may be subject to change. Applicants will be informed if there are any changes.

KC4009 -

Calculus (Core, 20 Credits)

The module is designed to introduce you to the principles, techniques and applications of calculus. The fundamentals of differentiation and integration are extended to include differential equations and multivariable calculus.

On this module you will learn:

Differentiation: derivative as slope and rate of change, standard derivatives; product, quotient, function of a function rules; implicit, parametric and logarithmic differentiation; maxima / minima, curve sketching; Maclaurin's and Taylor's series.

Integration: standard integrals, definite integrals, area under a curve; using substitution, partial fractions and by parts; applications (eg volumes, r.m.s. values).

Ordinary differential equations: Solution by direct integration. Solution of first order equations by separation of variables and use of an integrating factor. Solution of homogeneous and non-homogeneous second order equations with constant coefficients.

Functions of several variables: partial differentiation, Taylor's series in two variables, total first order change, analysis of errors, total rate of change, change of variables; stationary points, maxima / minima / saddle points of functions of two variables.

Method of Lagrange Multipliers: constrained maxima / minima, classification of stationary points.

Multiple integrals: double and triple integrals, change of order of integration, use of polar coordinates, simple applications.

More information

KC4014 -

Dynamics (Core, 20 Credits)

This module is designed to provide you with knowledge in a special topic in Applied Mathematics. This module introduces Newtonian mechanics developing your skills in investigating and building mathematical models and in interpreting the results. The following topics will be covered:

Mathematics Review
Euclidean geometry. Vector functions. Position vector, velocity, acceleration.
Cartesian representation in 3D-space. Scalar and vector products, triple scalar product.

Newton’s Laws
Inertial frames of reference. Newton's Laws of Motion. Mathematical models of forces (gravity, air resistance, reaction, elastic force).

Rectilinear and uniformly accelerated motion
Problems involving constant acceleration (e.g., skidding car), projectiles with/without drag force (e.g., parabolic trajectory, parachutist). Variable mass. Launch and landing of rockets.
Linear elasticity. Ideal spring, simple harmonic motion. Two-spring problems. Free/forced vibration with/without damping. Resonance. Real spring, seismograph.

Rotational motion and central forces
Angular speed, angular velocity. Rotating frames of reference.
Simple pendulum (radial and transverse acceleration). Equations of motion, inertial, Coriolis, centrifugal effects. Effects of Earth rotation on dynamical problems (e.g. projectile motion).
Principle of angular momentum, kinetic and potential energy. Motion under a central force. Kepler’s Laws. Geostationary satellite.

More information

KC4017 -

Particles, Waves and the Big Bang (Core, 20 Credits)

The module will introduce you to some of the key ideas of contemporary physics and to show how these ideas came about. After introducing the concept of (i) particle-wave duality, you will be introduced to (ii) oscillatory phenomena and wave motion, and to the fundamentals of the (iii) standard model of particle physics and the origin of particles during the formation of the universe.

Outline Syllabus (note this is indicative rather than prescriptive):

Wave-particle duality
Electromagnetic spectrum, black body radiation and the photoelectric effect.

Standard Model and the Big Bang
A qualitative introduction to the standard model of particle physics. An introduction to Feynman diagrams. Basic constituents of matter, such as quarks and leptons, their fundamental properties and interactions, and their origin at the creation of the universe. Introductory Cosmology. Microwave Background Radiation. Star formation. Types of stars. Stellar classification.

Waves and Oscillations
Free, damped and forced vibrations, resonance, coupled oscillators; the nature of travelling waves and transport of energy; types of waves including sound, water waves and light; interference, beats and standing waves; dispersion; simple diffraction phenomena.

Geometrical Optics
Phenomena in geometrical optics, interference and diffraction and their practical applications. Properties of optical systems. The dependence of geometrical optics on wave theory.

More information

KD4010 -

Electricity, Magnetism and Electronics (Core, 20 Credits)

This module will introduce you to fundamental electromagnetism, electrical circuit theory and analogue electronics. Through a combination of lectures, labs and

technology-enhanced resources, you will learn to analyse basic DC and AC circuits and to familiarise with fundamental electronic components such as operational

amplifiers and semiconductor diodes. This module will provide you with core knowledge, and experimental, numerical and analytical skills to tackle problems in electrical

and electronic principles, thus establishing firm foundations for future employability.


Electricity and Magnetism (25%)


Electric charge: conductors, insulators and semiconductors. Electrostatics: Coulomb's law and the electric field; Concept of electric potential and its relation to the electric

field; Energy stored in an electric field; Application to a capacitor and link to capacitance. Magnetostatics: Forces arising between wires carrying electric currents; concept

of the magnetic field; Ampere’s Law; geometrical statement of the Biot-Savart law; the B field around a wire; the right-hand rule.


DC and AC Circuit Theory (50%)


Introduction to ideal linear elements: resistor, inductor and capacitor. Transient currents across ideal elements. Current and voltage division rule. Applications of

superposition: Kirchhoff’s law.



Properties of sinusoidal and periodic waveforms, average, RMS values. Phasors and phasor diagrams, and j operator. Complex impedance, impedance diagrams.

Applications to series circuits. Power in AC circuits, power factor, apparent power, active power, and reactive power. Complex admittance and applications to parallel

circuits. Series and parallel RLC circuits. Frequency response and resonance in simple RLC circuits.


Analogue Electronics (25%)


Introduction to the properties of an ideal operational amplifier. Simple inverting and non-inverting applications using virtual earth principles. Properties and parameters of a

non-ideal op-amplifier including gain-bandwidth and off-sets. Op-amplifier applications including summing, integrator and differentiator. Linear and non-linear applications.

More information

KD4014 -

Research, Analysis and Presentation (Core, 20 Credits)

This module aims to introduce you to gathering research data from either laboratory or reference material, analysing the acquired data in an appropriate manner and then presenting the key findings. Formal training in experimental techniques acquired in this module will support your professional and personal skills.

Research
Research methods will demonstrate where and how to gather information; researching for knowledge and information which can be applied to generate solutions to real world problems. The ability to select from a number of research methods is important for example the ability to research a method to design simple laboratory tests.

Analysis
Correct use of units and symbols for physics and engineering along with the use of data analysis techniques. Specific techniques may include for example: mean and standard deviation, simple regressive techniques, log – log and log linear relationships, and error analysis. Simple measurement techniques for example measuring: velocity, voltage, current and power. Key factors in measurement include the need to analyse: accuracy, errors, resolution and the need for calibration.

Presentation
Key communication skills in report writing, lab book writing (of laboratory data), and the presentation of information both visually via graphs and diagrams, and using text. A number of key skills are in focus here namely the highlighting of key findings and drawing suitable conclusions from a piece of work. Both written and oral presentation skills are exemplified.

Computation
You will be introduced to suitable computational packages for data analysis and processing in physics and engineering, for example, ORCAD and MATLAB.

More information

KD4015 -

Experiments and Discovery (Core, 20 Credits)

Experimental work is an important component of physics and this module provides the student with the opportunity to learn and develop core skills in observing physical phenomena and in the analysis of the results of measurements.

Students will perform experiments in a series of laboratory sessions across a broad range of physics topics, gaining experience in the use of standard laboratory equipment used in physics and also on the importance of systematic observation of physical phenomena capturing results and analyzing data to derive appropriate conclusions. The module also introduces the student to the concept of data acquisition, analysis using a computer and computer control of experiments.

Learnings and skills developed in this module:
Experiments spanning mechanics, optics, electromagnetism, electricity, thermodynamics, atomic physics and quantum physics.
Experimental techniques including recording data, plotting results, linear and logarithmic axes, and line of best fit.
Data analysis: statistical treatment of data; systematic and random errors; and combination and propagation of errors.
Computational work including: data acquisition and instrument control using National Instruments LabVIEW; and data analysis using Microsoft Excel.
Writing scientific reports: planning, structure, diagrams, tables, graphs and writing style.

More information

KL5001 -

Academic Language Skills for Mathematics, Physics and Electrical Engineering (Optional, 0 Credits)

Academic skills when studying away from your home country can differ due to cultural and language differences in teaching and assessment practices. This module is designed to support your transition in the use and practice of technical language and subject specific skills around assessments and teaching provision in your chosen subject. The overall aim of this module is to develop your abilities to read and study effectively for academic purposes; to develop your skills in analysing and using source material in seminars and academic writing and to develop your use and application of language and communications skills to a higher level.

The topics you will cover on the module include:

• Understanding assignment briefs and exam questions.
• Developing academic writing skills, including citation, paraphrasing, and summarising.
• Practising ‘critical reading’ and ‘critical writing’
• Planning and structuring academic assignments (e.g. essays, reports and presentations).
• Avoiding academic misconduct and gaining credit by using academic sources and referencing effectively.
• Listening skills for lectures.
• Speaking in seminar presentations.
• Presenting your ideas
• Giving discipline-related academic presentations, experiencing peer observation, and receiving formative feedback.
• Speed reading techniques.
• Developing self-reflection skills.

More information

KC5028 -

Advanced Mathematics for Physics (Core, 20 Credits)

The module is designed to provide you with the advanced mathematical and statistical techniques required to underpin study of physics at level 5 and beyond. Techniques covered will include Matrices, Fourier Series and Fourier and Laplace Transforms, Probability distributions, and an introduction to vector calculus (including div, grad and curl).

Students will develop skills in the use of advanced mathematical and statistical techniques, applying suitable mathematical calculations over a range of key topics, including explaining how a periodic waveform can be represented as an infinite series of sinusoids, and applying Fourier Transforms. The concepts of the eigenvalue and eigenvectors of a matrix, and how these can be found by algebraic means will also be covered. Finally, students will be introduced to vector calculus and vector operators, including div, grad and curl, and the Kronecker delta and Levi-Civita epsilon.

Linear Algebra
Algebraic evaluation of the eigenvalues and eigenvectors of a matrix (i.e. Matrices to the level of eigenvalues and eigenvectors). Application to the solution of a system of linear ordinary differential equations.

Vector Calculus
Coordinate systems; line, surface and volume integrals; Vector operators Grad, Div and Curl; Gauss’ (Divergence) Theorem, Stokes’ Theorem; Introduction to Cartesian tensors. Applications of vector calculus.

Fourier Series and Fourier and Laplace Transforms
Fourier series and periodic functions. Full-range and half-range series. Even and odd functions. Coefficients in complex form. Application to the solution of partial differential equations by the method of separation of variables. Fourier Transforms. Laplace Transforms. The convolution theorem. An introduction to the solution of partial differential equations.

Probability Distributions
Sample space, types of events, definition of probability, addition and multiplication laws, conditional probability. Discrete probability distributions including Binomial, Poisson. Continuous probability distributions including the Normal distribution.

More information

KC5029 -

Space-Time and Electromagnetism (Core, 20 Credits)

The theory of Electromagnetism and its relativistic foundation is at the heart of modern physics and provides a fundamental paradigm for understanding contemporary physical theories. This module will introduce you to the fundamental concepts of Special Relativity, and to the origins and properties of electric and magnetic fields. A research inquiry approach will bring you through the step-by-step processes that led to the discovery of the Maxwell equations and understanding their relativistic nature.

Electrostatics and Magnetostatics
Coulomb's law and the electric field; Electric flux and Gauss' law; Circulation and electric potential; Calculating the field from the potential (gradient); Gauss law in differential form (divergence); Circulation law in differential form (curl); Poisson's and Laplace's equations and their solutions. Polarization, multi-pole expansion, electric potential of a dipole.
Definition of magnetic field and calculation of the force; Calculating the B field: the Biot-Savart law; Circulation and Ampere's law in differential form; Magnetic flux and Gauss law in differential form; Magnetic vector potential. Equation of motion of a charge in a electromagnetic field; cycloid motion; cyclotron frequency.
Electrical and magnetic fields in materials; Electrostatic fields and conductors (method of images); Electrostatic fields in dielectrics; Magnetostatic fields in materials.

Electrodynamics
Maxwell’s Equations. Ohm’s Law in differential form; Electromotive force; Electromagnetic induction, Faraday's law in differential form; Ampere-Maxwell law in differential form; Maxwell's equations and their solutions.
Electromagnetic Waves. Derivation from Maxwell's Equations; speed of light; Energy flow, Poynting vector. Electromagnetic wave polarisation; Incident, reflected and transmitted waves at plane interfaces.

Special Relativity
Einstein's postulates; Time dilation; Length contraction; Lorentz transformations; Light cone; Relativistic velocity transformation, energy-momentum relation; Twin paradox. Relativistic invariance of charge; Lorentz transformation of electromagnetic fields; EM of moving charges.

More information

KD5081 -

Theory, Computation and Experiment (Core, 20 Credits)

This module aims to equip physics students with the knowledge and transferable skills involved in computational methods and experimental techniques. Students will analyse and present experimental data, create computational models for appropriate physical systems and perform comparisons between theory and experiment. Quantitative, analytical and modelling training acquired in this module will support students’ professional and personal skills. This module offers the additional opportunity of research-orientated learning through a hands-on approach to analysing research-based data.

Experiments - Topics may include (note this is indicative rather than prescriptive):
1. Doppler Effect
2. Optical properties of semiconductors
3. Particle accumulation on a glass surface (c.f. sand particles on photovoltaic modules and link to Monte Carlo)
4. The heat engine
5. Hall Effect
6. Fundamentals properties of X-rays
7. Radioactive decay of ?, ? and ? particles
8. Microwave Diffraction
9. PID Control
10. Thermal Conductivity
11. Cosmic Ray Detection
12. Solar photovoltaic efficiency measurement.

Computation - Topics may include (note this is indicative rather than prescriptive):
1. Curve fitting (linear and non-linear), statistical analysis and data presentation
2. Matrices to the level of eigenvectors and eigenvalues
3. Discretisation and series analysis
4. Ordinary differential equations
5. Partial differential equations (links to stock market modelling, radioactivity, electrical and mechanical systems)
6. Thermal modelling
7. Probability distribution functions

More information

KD5082 -

Quantum Universe (Core, 20 Credits)

At very small scales, classical mechanics (Newton’s laws) breaks down and quantum mechanics must be used. This module introduces the foundations of quantum mechanics starting from the failure of classical physics to describe important experiments and the concept of wave-particle duality. Students are then introduced to the concept of a particle’s wave function and solving the Schrödinger equation for standard problems.

Key parts of quantum mechanics that are covered within the module include:

The Origins of Quantum Mechanics
Bohr model of the atom. Quantised nature of light and atomic spectra. Failure of classical mechanics to describe key experiments. The photoelectric effect. Young’s double slit experiment. Wave nature of particles. Concept of wave function and localisation. De Broglie equation. Heisenberg Uncertainty Principle. Quantum numbers and Pauli Exclusion Principle.

The Schrödinger Equation and Standard Solutions
Time dependent Schrödinger equation and general formulation. Wave function normalisation. Time independent Schrödinger equation. Boundary conditions. Infinite square well. Finite square well. Tunnelling through a potential barrier. Harmonic Oscillator. Three dimensional Schrödinger equation. Particle in a box. Hydrogen atom.

Matrix Mechanics
Postulates of quantum mechanics. Operators and representation of dynamical variables. Eigenfunctions and eigenvalues and linear combinations. Hamiltonian and operator representation of the Schrödinger equation. Hermitian operators. Expectation values. Commutating operators. Harmonic oscillator: raising and lowering operators. Angular momentum and spin. Time independent perturbation theory

Particle Physics
Fundamental Forces. Particle Classification and the Standard Model. Particle interactions, reactions and decays.

More information

KD5083 -

Semiconductor Physics (Core, 20 Credits)

The module is aimed at providing students with core knowledge and understanding in semiconductor physics. The module also gives students an opportunity to develop professional and intellectual skills by analysing and discussing key industrial aspects of semiconductor materials applications. On completion of the module, students will be able to: 1. Explain the structure of matter and properties of solids in terms of atomic and molecular bonding. 2. Discuss how the band theory of solids arises when the Schrödinger equation is applied to the behaviour of electrons in solids. 3. Analyse the electrical and magnetic behaviour of solids in terms of the behaviour of their constituent electrons. 4. Analyse the behaviour of semiconductor materials in terms of the properties and behaviour of electrons and holes. 5. Discuss the common semiconductor materials, processing, devices and applications.

More information

KD5084 -

Thermal and Nuclear Energy (Core, 20 Credits)

This module introduces students to fundamental knowledge in thermodynamics, statistical mechanics and nuclear physics with a focus on transferable skills through problem solving using mathematical modeling. This module also offers the opportunity to analyse nuclear energy power generation and environmental issues in a policy and wider sustainability context, strengthening students’ professional skills and values.

Classical Thermodynamics
Zeroth, first and second laws of thermodynamics, temperature scales, thermal energy and work, internal energy and heat capacity. Classical gas laws. Specific heat, thermal resistance and capacitance and dynamic thermal models of structures such as domestic properties. Thermal cycles, including Carnot, Rankine and Otto cycles; applications to heat engines and heat pumps. Thermodynamic efficiency of heat engines. Entropy, Enthalpy and Helmholtz and Gibbs free energies. Maxwell Relations and Thermodynamic Susceptibilities.

Statistical Mechanics
Kinetic theory of gases; derivation of gas laws, specific heat, and mass, momentum and energy transport coefficients. Statistical mechanical interpretation of entropy. Single and multiple-particle partition function and its relation to thermodynamics. Probability distributions, including Maxwell-Boltzmann, Fermi-Dirac and Bose-Einstein distribution functions.

Nuclear Energy
The structure of the nucleus, zone of stability and simple nuclear models. Both natural and artificially induced radioactivity, including alpha, beta and gamma radiation. Nuclear fission and nuclear reactors. Nuclear fusion including an introduction to solar nuclear processes and current and future nuclear reactors. Nuclear instrumentation. Nuclear safety.

Nuclear and Thermal Power Sources and their effect on the environment
Thermodynamic efficiency, losses, overall effect on society, Sankey diagrams and simple modelling tools such as the McKay 2050 pathways calculator.

More information

KL5001 -

Academic Language Skills for Mathematics, Physics and Electrical Engineering (Optional, 0 Credits)

Academic skills when studying away from your home country can differ due to cultural and language differences in teaching and assessment practices. This module is designed to support your transition in the use and practice of technical language and subject specific skills around assessments and teaching provision in your chosen subject. The overall aim of this module is to develop your abilities to read and study effectively for academic purposes; to develop your skills in analysing and using source material in seminars and academic writing and to develop your use and application of language and communications skills to a higher level.

The topics you will cover on the module include:

• Understanding assignment briefs and exam questions.
• Developing academic writing skills, including citation, paraphrasing, and summarising.
• Practising ‘critical reading’ and ‘critical writing’
• Planning and structuring academic assignments (e.g. essays, reports and presentations).
• Avoiding academic misconduct and gaining credit by using academic sources and referencing effectively.
• Listening skills for lectures.
• Speaking in seminar presentations.
• Presenting your ideas
• Giving discipline-related academic presentations, experiencing peer observation, and receiving formative feedback.
• Speed reading techniques.
• Developing self-reflection skills.

More information

KA5029 -

International Academic Exchange 1 (Optional, 60 Credits)

This module is designed for all standard full-time undergraduate programmes within the Faculty of Engineering and Environment and provides you with the option to study abroad for one semester as part of your programme.

This is a 60 credit module which is available between Levels 5 and 6. You will undertake a semester of study abroad at an approved partner University where you will have access to modules from your discipline, but taught in a different learning culture. This gives you the opportunity to broaden your overall experience of learning. The structure of study will be dependent on the partner and will be recorded for an individual student on the learning agreement signed by the host University, the student, and the home University (Northumbria).

Your study abroad semester will be assessed on a pass/fail basis. It will not count towards your final degree classification but, if you pass, it is recognised in your transcript as an additional 60 credits for Engineering and Environment Study Abroad Semester.

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KA5030 -

International Academic Exchange 2 (Optional, 120 Credits)

This module is designed for all standard full-time undergraduate programmes within the Faculty of Engineering and Environment and provides you with the option to study abroad for one full year as part of your programme.

This is a 120 credit module which is available between Levels 5 and 6. You will undertake a year of study abroad at an approved partner University where you will have access to modules from your discipline, but taught in a different learning culture. This gives you the opportunity to broaden your overall experience of learning. The structure of study will be dependent on the partner and will be recorded for an individual student on the learning agreement signed by the host University, the student, and the home University (Northumbria).

Your study abroad year will be assessed on a pass/fail basis. It will not count towards your final degree classification but, it is recognised in your transcript as a 120 credit Study Abroad module and on your degree certificate in the format – “Degree title (with Study Abroad Year)”.

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KF5000 -

Engineering and Environment Work Placement Year (Optional, 120 Credits)

This module is designed for all standard full-time undergraduate programmes within the Faculty of Engineering and Environment to provide you with the option to take a one year work placement as part of your programme.

You will be able to use the placement experience to develop and enhance appropriate areas of your knowledge and understanding, your intellectual and professional skills, and your personal value attributes, relevant to your programme of study, as well as accreditation bodies such as BCS, IET, IMechE, RICS, CIOB and CIBSE within the appropriate working environments. Due to its overall positive impact on employability, degree classification and graduate starting salaries, the University strongly encourages you to pursue a work placement as part of your degree programme.

This module is a Pass/Fail module so does not contribute to the classification of your degree. When taken and passed, however, the Placement Year is recognised both in your transcript as a 120 credit Work Placement Module and on your degree certificate.

Your placement period will normally be full-time and must total a minimum of 40 weeks.

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KF5001 -

Engineering and Environment Work Placement Semester (Optional, 60 Credits)

This module is designed for all standard full-time undergraduate programmes within the Faculty of Engineering and Environment to provide you with the option to take a one semester work placement as part of your programme.

You will be able to use the placement experience to develop and enhance appropriate areas of your knowledge and understanding, your intellectual and professional skills, and your personal value attributes, relevant to your programme of study, within the appropriate working environments. Due to its overall positive impact on employability, degree classification and graduate starting salaries, the University strongly encourages you to pursue a work placement as part of your degree programme.

This module is a Pass/Fail module so does not contribute to the classification of your degree. When taken and passed, however, the placement is recognised both in your transcript as a 60 credit Work Placement Module and on your degree certificate.

Your placement period will normally be full-time and must total a minimum of 20 weeks.

More information

KL5001 -

Academic Language Skills for Mathematics, Physics and Electrical Engineering (Optional, 0 Credits)

Academic skills when studying away from your home country can differ due to cultural and language differences in teaching and assessment practices. This module is designed to support your transition in the use and practice of technical language and subject specific skills around assessments and teaching provision in your chosen subject. The overall aim of this module is to develop your abilities to read and study effectively for academic purposes; to develop your skills in analysing and using source material in seminars and academic writing and to develop your use and application of language and communications skills to a higher level.

The topics you will cover on the module include:

• Understanding assignment briefs and exam questions.
• Developing academic writing skills, including citation, paraphrasing, and summarising.
• Practising ‘critical reading’ and ‘critical writing’
• Planning and structuring academic assignments (e.g. essays, reports and presentations).
• Avoiding academic misconduct and gaining credit by using academic sources and referencing effectively.
• Listening skills for lectures.
• Speaking in seminar presentations.
• Presenting your ideas
• Giving discipline-related academic presentations, experiencing peer observation, and receiving formative feedback.
• Speed reading techniques.
• Developing self-reflection skills.

More information

KC6028 -

Dynamical Systems (Optional, 20 Credits)

The module aims to present an introduction to Dynamical Systems and associated transferable skills, providing the students with tools and techniques needed to understand the dynamics of those systems. You will analyse non-linear ordinary differential equations and maps, focusing on autonomous systems, and will learn analytical and computational methods to solve them. This module offers the additional opportunity of research-orientated learning through a hands-on approach to selected research-based problems.

Topics may include (note this is indicative rather than prescriptive):
1. Autonomous linear systems, fixed points and their classification.
2. 1-dimensional non-linear systems: critical points; local linear approximations; qualitative analysis; linear stability analysis; bifurcations.
3. Multi-dimensional non-linear systems: linearisation about critical points, limit cycles, bifurcations.
4. Discrete systems: maps (such as tent map, logistic map, Henon map, standard map).
5. Numerical schemes for ordinary differential equations, such as the embedded Runge-Kutta method.
6. Numerical applications and programming: generation of the orbit of a map, Lorenz map for a dynamical system, orbit diagrams, cobwebs, simple fractals.
7. Elements of Chaos theory: Lyapunov exponents, sensitive dependence on initial conditions, strange attractors, Hausdorff dimension, self-similarity, fractals.

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KD6030 -

Optical Communications System Design (Optional, 20 Credits)

The module will provide the knowledge and skills for you in two key themes of optical fibre and optical wireless communications. These are essential topics for communications pathway in electrical and electronics engineering programme that cover the fundamentals and advanced optical system designs in both fibre and wireless systems. Optical fibre communications provides the backbone for long-haul and medium range telecommunications that offers ultrahigh data transmission capacity whereas optical wireless communications is an emerging technology that enables data transmission via light, either in infrared or visible light band using laser and/or light emitting diode (LED) for indoor and short range communications system.

Through the module syllabus you will learn:

Fundamental optical fibre/wireless communications includes
- Introduction to the optical wire/wireless communications system and the overall design
- Identification of system elements, subsystems and required specifications
- Optical transmitter design, optical propagation channel, effect on the optical fibre, effect on the optical wireless channel, noise and losses, optical receiver design.

System design includes: multiple access techniques, system design and performance evaluation, analysis of the practical and industrial optical communications system

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KD6031 -

Instrumentation and Control of Dynamical Systems (Core, 20 Credits)

This module shows you how to use modern control design techniques based on state-space differential equations governing a dynamical system. You will also cover instrumentation techniques that are required for practical implementation of control algorithms. Upon completion of the module, you will be able to design instrumentation and control systems; implement and evaluate them using relevant software packages. There are two main themes:

Control
Classical control design and analysis. PID control and pole placement methods, Bode and Nyquist plots, Laplace transforms and z-transforms. Modelling of dynamical systems including for example: magnetic levitation, chemical processes, sustainable energy systems, particle detection, satellite positioning and the gyroscope. State feedback control design: state-space representation of systems, linear controllability and observability and rank condition. Linear feedback control design. Stability: asymptotic and global asymptotic stability, Lyapunov stability and Lyapunov equation. Estimation: Luenberger observer design. Digital control: Different equations, sampling effect in computers, ADC, DAC, ZOH, Z-transfer function, compensator design, stability analysis. Use of Matlab and Simulink software for simulation of control algorithms. Systems representation of instrumentation systems. Modelling of measurement systems including the effects of sensors.

Instrumentation
Range, span, nonlinearity, hysteresis, resolution, ageing effects. Dynamic modelling of sensors using transfer functions and state-space methods. Signal conditioning: loading effects, bridge circuits, correction of non-linearity, effects of feedback, amplifier limitations. Noise and interference in instrumentation systems and estimation of errors. Signal recovery from noise interference. Computerised data acquisition systems including ADCs and a range of modern instrumentation protocols. Use of microcontrollers and inversion techniques. Use of Matlab and Simulink for simulation of instrumentation systems.

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KD6040 -

Individual Physics Project (Core, 40 Credits)

The module aims to provide the student, as an individual, an opportunity to carry out an extended study in a specific area of physics, developing the student's ability to work independently and promoting self-reliance. Guidance to source and assess the appropriateness of information is provided by the module.

A key aim is to encourage students to apply theoretical and analytical techniques to problem solve. The module also aims to develop both verbal and written communication skills. The project will provide practical experience of drawing up a project specification defining aims, objectives and identifying an envisaged endpoint. With their supervisor’s guidance, the student will prepare a project plan that includes a Gantt chart, project background and sourcing previous work and associated theory/simulation to assess whether the aims and objectives are achievable and that their theoretical basis is sound.

To meet University requirements and gain practical experience, students must perform a risk assessment to identify potential risks/hazards associated with the project. The student will follow the defined plan to complete the project that will include, for example, experimental investigations and the application of appropriate theory and simulations

Students will be encouraged to monitor their progress based upon the project plan and, where necessary, adjust timescales/objectives. The student will be required to submit a final project report and present the project verbally to the supervisor, second markers and peers. Contact with the supervisor must be maintained on a regular basis to: discuss/assess progress and obtain advice.

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KD6041 -

Quantum Devices (Core, 20 Credits)

Physicists are increasingly able to exploit quantum mechanical behaviour in new optoelectronic devices that will have a profound impact on our lives. These devices offer unprecedented performance in terms of speed and efficiency. The student will develop knowledge of how these characteristics stem from design at the atomic scale and of the challenges associated with scaling-up for practical applications such as sustainable energy and quantum computing.

Background Quantum Theory
Review of quantum mechanical concepts. Density of states function in one, two and three dimensions. Fermi-Dirac occupation function. Electron gas and the Fermi surface. Band theory of semiconductors and doping. Band structure of important semiconductors.

Low-dimensional Semiconductors
Energy and length scales. Fabrication techniques: top down and bottom up. High electron mobility transistor and the two-dimensional electron gas. Quantum Hall effect. Quantum wires and quantised conductance. Semiconductor quantum dots. Measurement methods for quantum devices.

Quantum Devices
Quantum computing. Quantum cryptography. Single photon and entangled photon emitters. Single electron transistor. Semiconductor quantum dot laser. Quantum cascade laser. Optical cavities. Third generation photovoltaics and quantum efficiency. Light emitting diodes and solid state lighting. Resonant tunnelling diode. Future opportunities for quantum devices: properties of graphene and graphene-based devices; Scaling up nanotechnology. Sustainability and cost.

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KD6042 -

Advanced Photovoltaics (Core, 20 Credits)

The photovoltaic (PV) effect is the direct conversion of sunlight into electricity. Future energy demand and climate change require a significant increase in renewable generation to sustain economic development. The power incident on the Earth from sunlight, vastly exceeds human consumption, PV offers the most viable route to sustainably generate electricity from the Sun. The module delivers an advanced understanding of solar photovoltaic technologies through the four main themes indicated below:

Solar Resource: Solar energy, including concepts such as Air Mass spectra and solar insolation.

Relevant semiconductor theory, to: understand the photovoltaic effect, the interaction of light with solar cell materials and the electrical behaviour of the materials. Subjects covered include, semiconductors under equilibrium conditions, direct and indirect energy bandgaps, optical absorption and electrical properties. Solar cells operate under non-equilibrium conditions and recombination processes, current density, minority carrier behaviour within ideal pn junctions and diodes, are examined within the module.

Solar cells are introduced, based on ideal photovoltaic solar cell key parameters: the Current-Voltage (I-V) characteristic, Spectral response and Capacitance-voltage behaviour. The optimum energy bandgap for a single junction solar cell is considered and then multi-junction solar cells and advanced concepts.

Commercially produced solar cells their applications and the PV market. A review of the design and manufacture of solar cells based on crystalline silicon, multicrystalline silicon, “low cost” thin film semiconductors, Graetzel , organic and high efficiency solar cells is included.

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KL5001 -

Academic Language Skills for Mathematics, Physics and Electrical Engineering (Optional, 0 Credits)

Academic skills when studying away from your home country can differ due to cultural and language differences in teaching and assessment practices. This module is designed to support your transition in the use and practice of technical language and subject specific skills around assessments and teaching provision in your chosen subject. The overall aim of this module is to develop your abilities to read and study effectively for academic purposes; to develop your skills in analysing and using source material in seminars and academic writing and to develop your use and application of language and communications skills to a higher level.

The topics you will cover on the module include:

• Understanding assignment briefs and exam questions.
• Developing academic writing skills, including citation, paraphrasing, and summarising.
• Practising ‘critical reading’ and ‘critical writing’
• Planning and structuring academic assignments (e.g. essays, reports and presentations).
• Avoiding academic misconduct and gaining credit by using academic sources and referencing effectively.
• Listening skills for lectures.
• Speaking in seminar presentations.
• Presenting your ideas
• Giving discipline-related academic presentations, experiencing peer observation, and receiving formative feedback.
• Speed reading techniques.
• Developing self-reflection skills.

More information

KD7028 -

Soft and Nanomaterials (Core, 20 Credits)

This module is aimed at equipping students with subject specialist knowledge at the forefront of research in soft and nano-materials. The module has a particular focus on developing professional skills linked to understanding and critically appraising the current landscape of research in soft condensed matter.

The content of the module is informed by research within the Faculty of Engineering and Environment including soft and biological matter physics and the application of quantum mechanics. Soft and biological matter physics involves concepts in fluid dynamics and statistical physics underpinning fluid dynamical systems at small scales including super-hydrophobic surfaces, microscopic motility and colloidal systems. The application of quantum mechanics is explored through nanostructures such as quantum dots, nanocrystals, nanowires, core-shell nanostructures. Furthermore, students are introduced to a range of techniques used to produce these nanostructures as well as characterization techniques.

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KD7030 -

Physics Research Project (Core, 60 Credits)

This module provides the student with an opportunity to demonstrate an integrated approach to the application of their specialist knowledge and skills within a physics-based research project supervised by an academic staff member engaged in active research in an area of physics. The student will be provided with an authentic research experience that will prepare them for further academic study or employment.

The student will work on an open-ended research problem focused on a topic at the forefront of physics research. They will gain competence in the use of specialist equipment, analysis techniques, specialist software packages and/or computer programming as required to complete the module. The student will have the opportunity to develop further communication skills through oral presentations and a dissertation. The academic level of the dissertation is aimed at suitability for submission to a peer-reviewed journal.

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KD7043 -

Further Mathematics for Physics (Core, 20 Credits)

This module is designed to provide the students with intellectual and professional skills in mathematics required to underpin the study of physics at level 7 (beyond BSc level). Hands-on training in mathematical techniques to model physical phenomena in this module is aimed at enhancing students’ employability and/or potential engagement in doctoral training.

The mathematical techniques covered include series solutions to ordinary differential equations, integral methods and solutions to inhomogeneous ordinary and partial differential equations, and calculus of variations. The module will also introduce students to advanced modeling techniques using specialist software, such as Matlab and Mathematica.

I. Series solutions of ordinary differential equations. Legendre polynomials, Bessel functions, sets of orthogonal functions.

II. Integral methods for ordinary and partial differential equations. Green’s functions, application to solutions of differential equations.

III. Calculus of variations. Functionals, variations and functional derivatives, extrema, Euler-Lagrange equations.

IV. Advanced computer-assisted modelling. Formulation and solution of mathematical problems linked to parts I-III using specialist software, such as Matlab and Mathematica.

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KL5001 -

Academic Language Skills for Mathematics, Physics and Electrical Engineering (Optional, 0 Credits)

Academic skills when studying away from your home country can differ due to cultural and language differences in teaching and assessment practices. This module is designed to support your transition in the use and practice of technical language and subject specific skills around assessments and teaching provision in your chosen subject. The overall aim of this module is to develop your abilities to read and study effectively for academic purposes; to develop your skills in analysing and using source material in seminars and academic writing and to develop your use and application of language and communications skills to a higher level.

The topics you will cover on the module include:

• Understanding assignment briefs and exam questions.
• Developing academic writing skills, including citation, paraphrasing, and summarising.
• Practising ‘critical reading’ and ‘critical writing’
• Planning and structuring academic assignments (e.g. essays, reports and presentations).
• Avoiding academic misconduct and gaining credit by using academic sources and referencing effectively.
• Listening skills for lectures.
• Speaking in seminar presentations.
• Presenting your ideas
• Giving discipline-related academic presentations, experiencing peer observation, and receiving formative feedback.
• Speed reading techniques.
• Developing self-reflection skills.

More information

KL7001 -

Advanced Condensed Matter (Core, 20 Credits)

This module provides an overview of the physics of condensed matter systems which includes the macroscopic and microscopic properties of matter. A feature of this module is that it considers both hard and soft condensed matter and during the module, you will encounter many interesting phenomena involving quantum mechanics and statistical physics with numerous real-world examples throughout.

Outline Syllabus

1. Introduction

Condensed matter: solids, liquids and gases. Differences between phases: gases as disordered phases, emergence of spatial correlations in liquids, the broken symmetry and rigidity of crystals. Qualitative description of microscopic interactions: energy scales, van der Waals attraction and hard-sphere repulsion, the Lennard-Jones potential, molecular bonding, the hydrogen molecule, molecular orbitals, energy-band theory.

2. Structure of condensed matter

Probing condensed matter: Bragg’s scattering, scattering of photons, neutrons and electrons. Correlation functions: application to gases, liquids, and crystals. The symmetry and structure of crystals: lattices and space groups. Beyond gases, liquids and crystalline solids: liquid crystals, quasi-crystals and ordered magnets.

3. Thermodynamics and statistical physics

The laws of Thermodynamics, Thermodynamic variables and potentials. Equations of state. Phase coexistence and stability. Phase space and thermodynamic ensembles. Connection between statistical physics and thermodynamics.

4. Statistical description of condensed matter systems

Spatial correlations. Ordered systems. Symmetry and order parameters. Mean field theories: Bragg-Williams theory; Landau theory and the Ginzburg-Landau potential; The Ising model. Application: solution of the Ising model using the Montecarlo method. The liquid-gas phase transition: the critical point and the coexistence curve. Multivariate systems: bicritical, tricritical and tetracritical points. The solid-liquid phase transition. Qualitative description of critical phenomena: critical exponents, universality and scaling

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