Module code: PHY3044

Module provider


Module Leader

GINOSSAR E Dr (Physics)

Number of Credits


ECT Credits



FHEQ Level 6

JACs code


Module cap (Maximum number of students)


Module Availability

Semester 1

Overall student workload

Independent Study Hours: 117

Lecture Hours: 33

Assessment pattern

Assessment type Unit of assessment Weighting
Coursework COURSEWORK 30%

Alternative Assessment


Prerequisites / Co-requisites

Module overview

A FHEQ Level 6 course that reviews the basic principles of quantum mechanics, and develops the following more advanced concepts; Dirac notation, operator methods, orbital and spin angular momentum, a detailed solution of the electronic structure of the Hydrogen atom, matrix mechanics, addition of angular momenta, identical particle symmetry, approximation methods such as the variational method and time independent perturbation theory, time dependent perturbation theory, Fermi’s Golden rule and its applications.

Module aims

To develop a detailed understanding of the postulates of quantum mechanics, and operator methods. The principles learned here will be applied to a variety of problems that can be solved analytically. The module goes beyond analytically soluble problems by introducing a variety of approximation methods.

Learning outcomes

Attributes Developed
Recall the postulates of quantum mechanics, and apply them to simple two level systems KC
Be able to use operators and commutation relations in analysing the simple harmonic oscillator, angular momentum and spin C
Represent operators as matrices KC
Recognise the analytic solution of the hydrogen atom K
Apply approximation methods including perturbation theory to calculate the effect of non-analytic terms such as an electric field KC

Attributes Developed

C - Cognitive/analytical

K - Subject knowledge

T - Transferable skills

P - Professional/Practical skills

Module content

Review of Quantum Physics: Problems in Classical physics, Dirac notation, Postulates of Quantum Mechanics, operators, compatible and incompatible observables, Quantum numbers, Uncertainty Principle, expectation values.
Simple Harmonic Oscillator: Solve using operators, raising and lowering operators, commutation relations, ground state, excited states. 
Schrödinger's Equation in 3D: Separation of variables in Cartesian coordinates, 3D infinite-square well, Central potentials, reduction to 1D problem, 3D simple harmonic oscillator, 3D Spherical well, degenerate states.
Angular Momentum: Commuting observables  and , Raising and lowering operators, eigenstates and eigenvalues of angular momentum operators, parity of eigenfunctions, excitation spectrum of a diatomic molecule.  
The Hydrogen Atom: Solution by dimensional analysis, Exact solution of the Hydrogen atom, quantum numbers Radial and Azimuthal wavefunction, accidental degeneracy.
Spin and Matrix Mechanics: Stern-Gerlach experiment, spin angular momentum, Matrix mechanics, angular momentum in matrix form, general matrix representation. 
Addition of Angular momenta: Total angular momentum, raising and lowering operators, combining spin and orbital angular momentum, combining two spin angular momenta, constructing the eigenstates of  and  .
Identical particle symmetry: Pair exchange operator, Spin-statistics theorem, Fermions and Bosons, symmetrising wavefunctions, Pauli exclusion principle, symmetrising spin and space wavefunctions.
Approximation Methods: Variational method for upper bound on ground state energy, Time-independent perturbation theory, first and second order energy corrections. Time-dependent perturbation theory, Fermi’s Golden rule, and applications to Einstein’s A&B coefficients, dipole selection rules, and scattering theory.

Methods of Teaching / Learning

The learning and teaching strategy is designed to:

Enable students to understand the physics concepts involved in Quantum Mechanics, how to use mathematical tools to find analytical solutions, and to go beyond these analytical solutions using approximation methods.

The learning and teaching methods include:

3 hours of lectures per week x 11 weeks.  Problem sets will be issued throughout the course to give practice at problem-solving.


Assessment Strategy

The assessment strategy is designed to provide students with the opportunity to demonstrate their ability to recall and apply the postulates and the methods of quantum mechanics to simple systems. The student will understand how to use operator methods to analyse the simple harmonic oscillator, and angular momentum. The student will be able to represent operators as matrices and use standard matrix methods, for example to compute the eigenvalues and expectation values of operators. The student will also be able to go beyond exact solution methods, and apply approximation methods such as perturbation theory, and variational method to simple systems.


Thus, the summative assessment for this module consists of:

·         coursework, which will take about 20 hours of effort, weighted at 30%

·         A final examination of 1.5h duration, with 2 questions from 3 to be attempted, allowing the student the opportunity to show basic recall of the course, derive some key results, and demonstrate their problem solving ability.


Formative assessment and feedback

Weekly problem sets are issued during the course, with tutorials scheduled throughout the semester. At least one of these problem sets will be formally marked and handed back to the student with explicit written feedback.

Reading list


Please note that the information detailed within this record is accurate at the time of publishing and may be subject to change. This record contains information for the most up to date version of the programme / module for the 2017/8 academic year.