University of St Andrews

Key information

SCOTCAT credits : 15

ECTS credits : 7

Level : SCQF level 11

Semester: Both

Availability restrictions: Normally only taken in the final year of an MPhys or MSci programme involving the School

Planned timetable: 2.00 pm Mon & Tue, 3.00 pm Thu

This module consists of seven parts: (i) classical and quantum systems; (ii) vector spaces, Hilbert spaces, operators and probability; (iii) basic postulates of quantum mechanics for observables with discrete spectra; (iv) illustrative examples; (v) treatment of continuous observables in terms of probability distribution functions and the spectral functions; (vi) quantum theory of orbital and spin angular momenta, Pauli-Schrodinger equation and its applications; (vii) introduction to relativistic quantum mechanics.

Relationship to other modules

Pre-requisite(s): Before taking this module you must ( pass PH3081 or pass PH3082 or pass MT2506 and pass MT2507 ) and pass PH3061 and pass PH3062

Learning and teaching methods and delivery

Weekly contact: 3 lectures or tutorials.

Scheduled learning hours: 32

Guided independent study hours: 118

Assessment pattern

As used by St Andrews: 2-hour Written Examination = 100%

As defined by QAA
Written examinations : 100%
Practical examinations : 0%
Coursework: 0%

Re-assessment: Oral Re-assessment, capped at grade 7

Personnel

Module coordinator: Dr K K Wan
Module teaching staff: Dr K Wan
Module coordinator email kw@st-andrews.ac.uk

Additional information from school

The emphasis is on developing a good understanding of the mathematical and conceptual foundations of the subject.  Hilbert spaces, operators, the spectral theorem and the basic postulates of quantum mechanics are discussed in detail.  The theory is illustrated by a detailed study of harmonic oscillator, orbital and spin angular momenta.  An introduction of relativistic quantum mechanics is presented.

 

Learning Outcomes

Having taken the module students should have gained a good knowledge of the mathematical techniques employed in modern physics and a good understanding of quantum mechanics in an axiomatic manner. In particular students should have a good knowledge of

 

• operator theory in Hilbert space, particularly selfadjoint and unitary operators, projectors and the spectral theorem for selfadjoint operators and properties of commuting selfadjoint operators,
• the basic postulates on quantum statics and dynamics, including the working of various Pictures to describe quantum evolution, and some conceptual issues,
• the use of creation and annihilation operators,
• operator theory of orbital and spin angular momenta,
• charged spin-half particle in external magnetic field,
• Klein-Gordon and the Dirac equations and the relativistic origin of spin.

 

Synopsis

The module is presented in several parts:

Part 1 is a review of general properties of classical and quantum systems,

Part 2 introduces Hilbert spaces starting from finite-dimensional vector spaces, and operators in Hilbert spaces, including selfadjoint operators, unitary operators, projectors, and the spectral theorem.

Part 3 sets out the basic postulates of quantum mechanics, illustrated by many examples and applications, including quantum evolution in terms Schrodinger, Heisenberg and Interaction pictures. Conceptual issues such as nonlocality, quantum entanglement, quantum paradoxes and measurement problems are also discussed.

Part 4 consists of illustrative examples which include a study of the harmonic oscillator and a general review of annihilation and creation operators and their application to harmonic oscillator.

Part 5 presents a systematic treatment of position and momentum as continuous observables.

Part 6 discusses operator theory of angular momentum, including orbital and spin angular momenta and application to the Zeeman effect and the Aharonov-Bohm effect..

Part 7 introduces relativistic quantum mechanics, including the Klein-Gordon and the Dirac Equations and the relativistic origin of spin.

 

Recommended Books

Please view University online record:

http://resourcelists.st-andrews.ac.uk/modules/ph5002.html

 

General Information

Please also read the general information in the School's honours handbook that is available via st-andrews.ac.uk/physics/staff_students/timetables.php.