Module code: PHY3044

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 provider

Physics

GINOSSAR Eran (Physics)

Module cap (Maximum number of students): N/A

Independent Learning Hours: 117

Lecture Hours: 33

Semester 1

Prerequisites / Co-requisites

Essential Mathematics ( BSc Physics Year 1 equivalent) Mathematical and Computational Physics (BSc Year 1 equivalent) Quantum physics ( BSc Physics Year 2 equivalent) Atoms and Light ( BSc Physics Year 2 equivalent)

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.

Assessment pattern

Assessment type Unit of assessment Weighting
Coursework COURSEWORK 30
Examination END OF SEMESTER 2HR EXAMINATION 70

None.

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%

·         2.0 hour examination at the end of the semester (70%), with a section A of compulsory questions and a section B with 2 questions chosen from 3. In Part A answer all questions (40 points); In Part B answer two questions out of three (10-points each). If all three questions in Part B are attempted only the best two will be counted.

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.

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 1 Recall the postulates of quantum mechanics, and apply them to simple two level systems KC 2 Be able to use operators and commutation relations in analysing the simple harmonic oscillator, angular momentum and spin C 3 Represent operators as matrices KC 4 Recognise the analytic solution of the hydrogen atom K 5 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

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.

Indicated Lecture Hours (which may also include seminars, tutorials, workshops and other contact time) are approximate and may include in-class tests where one or more of these are an assessment on the module. In-class tests are scheduled/organised separately to taught content and will be published on to student personal timetables, where they apply to taken modules, as soon as they are finalised by central administration. This will usually be after the initial publication of the teaching timetable for the relevant semester.

Upon accessing the reading list, please search for the module using the module code: PHY3044

Programmes this module appears in

Programme Semester Classification Qualifying conditions
Physics with Nuclear Astrophysics MPhys 1 Optional A weighted aggregate mark of 40% is required to pass the module
Physics with Astronomy MPhys 1 Optional A weighted aggregate mark of 40% is required to pass the module
Physics MSc 1 Optional A weighted aggregate mark of 40% is required to pass the module
Physics with Nuclear Astrophysics BSc (Hons) 1 Optional A weighted aggregate mark of 40% is required to pass the module
Physics with Astronomy BSc (Hons) 1 Optional A weighted aggregate mark of 40% is required to pass the module
Physics with Quantum Technologies MPhys 1 Optional A weighted aggregate mark of 40% is required to pass the module
Physics with Quantum Technologies BSc (Hons) 1 Optional A weighted aggregate mark of 40% is required to pass the module
Physics BSc (Hons) 1 Optional A weighted aggregate mark of 40% is required to pass the module
Physics MPhys 1 Optional A weighted aggregate mark of 40% is required to pass the module
Liberal Arts and Sciences BA (Hons)/BSc (Hons) 1 Optional A weighted aggregate mark of 40% is required to pass the module
Mathematics and Physics BSc (Hons) 1 Optional A weighted aggregate mark of 40% is required to pass the module
Mathematics and Physics MPhys 1 Optional A weighted aggregate mark of 40% is required to pass the module
Mathematics and Physics MMath 1 Optional A weighted aggregate mark of 40% is required to pass the module

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 2020/1 academic year.