KD5082 - Quantum Universe

What will I learn on this module?

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.

How will I learn on this module?

A wide range of learning and teaching approaches are used in this module. Lectures allow students to experience and understand the mathematical formalism of quantum mechanics and include relevant examples. Students have an opportunity to enhance their understanding of the subject through seminars which promote independent learning and tackle rich problems in quantum mechanics. Students are provided with formative feedback to problems in seminars and have the opportunity to problem solve within peer groups. Technology is also used to enhance students learning as solutions to the Schrödinger equation are routinely visualised in software. In addition, students are encouraged to use an online resource from the Institute of Physics (www.quantumphysics.iop.org) designed to support the undergraduate university curriculum.

Summative assessment is composed of an assignment (worth 30% of the module mark) and a closed book written examination (worth 70% of the module mark). The assignment is composed of diverse questions that allow students to reflect on their understanding of quantum mechanics. Feedback is provided to students both individually and in a plenary format to help students improve and promote dialogue around the assessment. The examination requires students to analyse and solve problems using both calculation and written arguments.

A further assessment tool is centred on technology enhanced learning and involves formative online quizzes. These are made available to students via the e-learning portal and provide immediate feedback. The quizzes are intended to focus on conceptual aspects of quantum mechanics rather than mathematical rigour and therefore allow students to reflect on their subject grasp.

How will I be supported academically on this module?

In addition to direct contact with the module team during lectures and seminars, students are encouraged to develop their curiosity by making direct contact with the module team either via email or the open door policy operated throughout the programme. Students will also be regularly referred to supporting resources including relevant texts and multimedia relevant to quantum mechanics. References to these resources will be made available through the e-learning portal and in lectures and seminars.

What will I be expected to read on this module?

All modules at Northumbria include a range of reading materials that students are expected to engage with. Online reading lists (provided after enrolment) give you access to your reading material for your modules. The Library works in partnership with your module tutors to ensure you have access to the material that you need.

What will I be expected to achieve?

Knowledge & Understanding:
• Appreciate the failure of classical physics to account for experimental results and the concept of wave-particle duality

Intellectual / Professional skills & abilities:
• Apply the time independent Schrödinger equation to solve important examples
• Apply a matrix representation of the Schrödinger equation and other quantum mechanical problems involving spin and angular momentum

Personal Values Attributes (Global / Cultural awareness, Ethics, Curiosity) (PVA):
• Increase capacity for curiosity through the concept of measurement in quantum mechanics

How will I be assessed?

SUMMATIVE
1. Assignment (30%) – KU1
2. Examination (70%) – ISA1, ISA2, PVA1

FORMATIVE
1. Seminar problems ISA1, ISA2
2. Online quizzes KU1, PVA1

Feedback is provided to students individually and in a plenary format both written and verbally to help students improve and promote dialogue around the assessment. Online feedback is also provided immediately.

Pre-requisite(s)

N/A

Co-requisite(s)

N/A

Module abstract

Quantum technologies such as quantum computing offer unprecedented power and the potential to solve some of the world’s most challenging problems. These technologies are underpinned by the laws of quantum mechanics which are drastically different from classical physics. For example, a sub-atomic particle can be in a combination of two states at the same time as famously illustrated via Schrödinger’s cat analogy. In this module you will learn the fundamental laws and mathematical principles of quantum mechanics. The module content is regularly informed by research activities within the Faculty and beyond. Furthermore, a range of software tools are used to enhanced your learning experience, throughout. Building on problems tackled in seminars, you will complete an assignment that covers problems in quantum mechanics and provides you with the opportunity to research a compelling quantum mechanical phenomenon. These module enables you to develop invaluable skills for progressing you career as a professional physicist in a wide variety of sectors and industries.

Course info

UCAS Code Z028

Credits 20

Level of Study Undergraduate

Mode of Study 4 years Full Time or 5 years with a placement (sandwich)/study abroad

School Engineering, Physics and Mathematics

Location City Campus, Northumbria University

City Newcastle

Start September 2027

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Module Information

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