Unit information: Quantum Mechanics in 2013/14

Unit name	Quantum Mechanics
Unit code	MATH35500
Credit points	20
Level of study	H/6
Teaching block(s)	Teaching Block 2 (weeks 13 - 24)
Unit director	Professor. Linden
Open unit status	Not open
Pre-requisites	MATH20100 and MATH21900
Co-requisites	None
School/department	School of Mathematics
Faculty	Faculty of Science

Description including Unit Aims

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. 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.

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.

syllabus

• motivation
• time-dependent and time-independent Schroedinger equations with characteristic examples including square wells and barriers (illustrating bound and scatttering systems and tunneling) and the harmonic oscillator
• the mathematical structure of quantum mechanics, including Hilbert space as state space, observables as self-adjoint operators and the probabilistic interpretation of quantum states
• commutation relations and the uncertainty principle
• unitary transformations, including time evolution
• measurement
• classical/quantum correspondence
• angular momentum and spin
• the Einstein-Podolsky-Rosen paradox and Bells inequalities

Relation to Other Units

This unit cannot be taken by students who have taken or are taking relevant physics units at either level 2 or level 3. 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.

Intended Learning Outcomes

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.

Teaching Information

Lectures, problem sheets

Assessment Information

The assessment mark for Quantum Mechanics is calculated from a 2½-hour written examination in May/June consisting of FIVE questions. A candidate's best FOUR answers will be used for assessment. Calculators are NOT permitted for this examination.

Reading and References

• K. Hannabuss, An Introduction to Quantum Theory, Oxford 1997

Students may also find the following books interesting for further reading:

• C. J. Isham, Lectures on Quantum Theory, Imperial College Press, 1995

• A. Peres, Quantum Theory: Concepts and Methods, Kluwer, 1995