PHYM422 Quantum Physics III

2007-2008

Code: PHYM422
Title: Quantum Physics III
Instructors: Prof. A.K. Savchenko
CATS credits: 10
ECTS credits: 5
Availability: unrestricted
Level: M
Pre-requisites: Quantum Physics II (PHY3030)
Co-requisites: N/A
Background Assumed: -
Duration: Semester II
Directed Study Time: 22 lectures
Private Study Time: 78 hours
Assessment Tasks Time: -
Observation report: 2001/02 IRS

Aims

The purpose of this module is to reinforce and build upon the foundations laid in PHY2002 and PHY3030. The module covers a range of more advanced topics leading to the discussion of quantum transitions and non-relativistic scattering. Much of physics concerns manifestations of the electromagnetic interaction which is susceptible to perturbation techniques. The methods outlined in the module are applicable to many situations in condensed matter and nuclear physics enabling useful and informative solutions to be obtained to non-exactly-soluble problems without resort to numerical methods.

Intended Learning Outcomes

A student should be able to:

Module Specific Skills

• formulate, and evaluate, the solutions to a variety of perturbed quantum mechanical systems;
• calculate energy shifts, transition probabilities (and rates) and cross-sections.

Discipline Specific Skills

• use mathematics to solve problems;
• present and defend their solutions to problems to the group.

Personal and Key Skills

• undertake co-operative learning by discussing the contents of the module amongst themselves;
• make informal presentations of technical material;
• work independently in order to meet deadlines.

Learning and Teaching Methods

Lectures and group discussions (20×1hr), directed reading, problems classes (2×1hr).

Assignments

Solve and prepare answers to problem sets issued for each topic in advance of class discussion.

Assessment

One 90-minute examination (100%).

Syllabus Plan and Content

The module is divided into a series of segments as indicated below. Each segment is supported by resource material, including a work plan, indicating how students should spend their time in working through the material and tackling the problems. Each segment will be supported by lectures and class discussions of completed problems.

1. Non-degenerate Perturbation Theory (2 weeks)
   1. Introduction
   2. Mathematical basis
   3. Perturbation method
   4. Sequence of perturbation equations
   5. Solution of first-order equation
   6. First-order result for change to energies and wavefunctions
   7. Second-order energy shifts
   8. Anharmonic oscillator
   9. Finite-nucleus correction
2. Degenerate Perturbation Theory (1 week)
   1. Introduction
   2. "Almost degenerate" limit of nondegenerate perturbation theory
   3. Solution of the problem of a doubly degenerate state
   4. Stark effect
3. Quantum Transitions (2 weeks)
   1. Introduction
   2. Time-dependent perturbation theory
   3. First-order theory
   4. Constant perturbation from t = 0
   5. Energy conservation
   6. Transition rate, Fermi's golden rule
   7. Harmonic perturbation and induced energy changes to a quantum system
4. Two-particle Systems (2 weeks)
   1. Noninteracting particles
   2. Helium atom
   3. Exchange interaction
   4. Spin eigenvalues and eigenfunctions for two electrons
   5. Spin wave functions and interchange symmetry
   6. Hydrogen molecule
5. Nonrelativistic scattering theory (3 weeks)
   1. Incident and scattered waves
   2. Integral equation
   3. Scattering amplitude
   4. Phase shifts
   5. Differential cross section
   6. Total cross section
   7. Born approximation

Core Text

McMurry S.M. (1994), Quantum Mechanics, Addison Wesley, ISBN 0-201-54439-3 (UL: 530.12 MCM)

Supplementary Text(s)

Open University Science Foundation Course Team (1988), Quantum Mechanics: An introduction, Open University (UL: 500 OPE/X)
Open University SM355 Course Team (1986), Quantum Mechanics: Units 12-14, Open University (UL: 530.12 OPE/X)
Open University SM355 Course Team (1986), Quantum Mechanics: Units 15-16, Open University (UL: 530.12 OPE/X)
Park D. (1974), Introduction to the Quantum Theory (2^nd edition), McGraw-Hill (UL: 530.12 PAR)
Pauling L. and Wilson E.B. (1935), Introduction to Quantum Mechanics, McGraw-Hill (UL: 530.12 PAU)
Rae A.I.M. (2007), Quantum Mechanics (5^th edition), Chapman and Hal, ISBN 1-584-88970-5 (UL: 530.12 RAE)

Formative Mechanisms

Students will be able to monitor their own progress using feedback provided in class.

Evaluation Mechanisms

The module will be evaluated using information gathered via the student representation mechanisms, the staff peer appraisal scheme, and measures of student attainment based on summative assessment.