Unit name | Quantum Mechanics |
---|---|

Unit code | MATH35500 |

Credit points | 20 |

Level of study | H/6 |

Teaching block(s) |
Teaching Block 1 (weeks 1 - 12) |

Unit director | Professor. Wiggins |

Open unit status | Not open |

Pre-requisites |
Either MATH20101 Ordinary Differential Equations 2 or MATH20402 Applied Partial Differential Equations 2 |

Co-requisites |
None |

School/department | School of Mathematics |

Faculty | Faculty of Science |

**Unit Aims**

The aim of the unit is to provide mathematics students with a thorough introduction to nonrelativistic quantum mechanics, with emphasis on the mathematical structure of the theory. Additionally, in conjunction with other units, it should provide suitably able and inclined students with the necessary background for further study and research at the postgraduate level. Two relevant research fields, namely quantum chaos and quantum information theory are at present strongly represented in the Mathematics Department and in the Science Faculty as a whole.

**Unit Description**

Quantum mechanics forms the foundation of 20th century and present-day physics, and most contemporary disciplines, including atomic and molecular physics, condensed matter physics, high-energy physics, quantum optics and quantum information theory, depend essentially upon it. Quantum mechanics is also the source and inspiration for various fields in mathematical physics and pure mathematics.

**Relation to Other Units**

This unit cannot be taken by students who have taken or are taking relevant physics units at either Level 5 or Level 6. For mathematics students, it is a prerequisite for the Level M unit Quantum Chaos and a useful preparation for the Level M unit Quantum Information Theory.

Learning Objectives

At the end of the unit the student should:

- be familiar with the time-independent and time-dependent Schroedinger equations, and be able to solve them in simple examples
- be familiar with the notions of Hilbert space, self-adjoint operators, unitary operators, commutation relations, understand their relevance to the mathematical formulation of quantum mechanics and be able to use the notions to formulate and solve problems
- understand the probabilistic interpretation of quantum states, and basic aspects of the relation between classical and quantum mechanics
- understand the quantum mechanical description of angular momentum and spin

Transferable Skills

Expressing physical axioms mathematically and analysing their consequences.

The unit will be taught through a combination of

- synchronous online and, if subsequently possible, face-to-face lectures
- asynchronous online materials, including narrated presentations and worked examples
- guided asynchronous independent activities such as problem sheets and/or other exercises
- synchronous weekly group problem/example classes, workshops and/or tutorials
- synchronous weekly group tutorials
- synchronous weekly office hours

90% Timed, open-book examination 10% Coursework

Raw scores on the examinations will be determined according to the marking scheme written on the examination paper. The marking scheme, indicating the maximum score per question, is a guide to the relative weighting of the questions. Raw scores are moderated as described in the Undergraduate Handbook.

If you fail this unit and are required to resit, reassessment is by a written examination in the August/September Resit and Supplementary exam period.

**Recommended**

- Keith Hannabuss,
*An Introduction to Quantum Theory*, Oxford 1997

**Further**

- C. J. Isham,
*Lectures on Quantum Theory*, Imperial College Press, 1995 - Asher Peres,
*Quantum Theory: Concepts and Methods*, Kluwer, 1995