Description

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.

Module Aims

The aim of this module is to build upon the foundations laid in PHY2022 Quantum Mechanics I and develop the students' grasp of quantum mechanics - particularly its formalism and applications - to the point where they will be able to engage with contemporary research literature.

Intended Learning Outcomes (ILOs)

A student who has passed this module should be able to:

• Module Specific Skills and Knowledge:
  1. formulate, and evaluate, the solutions to a variety of perturbed quantum mechanical systems;
  2. calculate energy shifts, transition probabilities (and rates) and cross-sections;
• Discipline Specific Skills and Knowledge:
  3. use matrix concepts to solve QM problems;
  4. use mathematics to solve problems;
  5. present and defend their solutions to problems to the group;
• Personal and Key Transferable / Employment Skills and Knowledge:
  6. undertake co-operative learning by discussing the contents of the module amongst themselves;
  7. make informal presentations of technical material;
  8. work independently in order to meet deadlines.

Syllabus Plan

1. Heisenberg's Approach to Quantum Mechanics
   1. Matrix elements for a quantum harmonic oscillator and a quantum rotor
   2. Electron spin and Pauli matrices
   3. Quantum particle in a double-well potential as a two-level system
2. Time-Independent Perturbation Theory
   1. Formulae for energy shifts to the first and second order
3. Atoms in External Fields
   1. Normal and anomalous Stark effect
   2. Spin-orbit interaction, normal and anomalous Zeeman effect
4. Few-Particle Systems
   1. Bose and Fermi particles, the Pauli principle
   2. Two-electron system: spin addition and exchange interaction
5. Structure of Many-Electron Atoms
   1. Electron shells
   2. Hund's rules,
   3. The role of spin-orbit interaction
   4. LS coupling scheme.
   5. Zeeman effect in many-electron atoms
   6. Hyperfine structure of atomic spectra.
6. Molecules
   1. Heitler-London theory
   2. Structure of molecular spectra
7. Quantum Transitions
   1. Perturbation theory
   2. Rabi oscillations
   3. Fermi's golden rule formula.
   4. The ammonia maser
   5. Rate of spontaneous emission.
8. Quantum Scattering
   1. Born approximation.
   2. Scattering of electrons in graphene

Learning and Teaching

Learning Activities and Teaching Methods

Assessment

Resources

The following list is offered as an indication of the type & level of information that students are expected to consult. Further guidance will be provided by the Module Instructor(s).

Core text:

• Rae A.I.M. (2007), Quantum Mechanics (5^th edition), Chapman and Hal, ISBN 1-584-88970-5

Supplementary texts:

• Eisberg R.M. and Resnick R. (1974), Quantum Physics of Atoms, Molecules, Solids, Nuclei and Particles, Wiley, ISBN 0-471-23464-8
• McMurry S.M. (1994), Quantum Mechanics, Addison Wesley, ISBN 0-201-54439-3
• Open University Science Foundation Course Team (1988), Quantum Mechanics: An introduction, Open University
• Open University SM355 Course Team (1986), Quantum Mechanics: Units 12-14, Open University
• Open University SM355 Course Team (1986), Quantum Mechanics: Units 15-16, Open University
• Park D. (1974), Introduction to the Quantum Theory (2^nd edition), McGraw-Hill
• Pauling L. and Wilson E.B. (1935), Introduction to Quantum Mechanics, McGraw-Hill

ELE:

• http://newton.ex.ac.uk/redirects/ELE/phym002

Further Information

Prior Knowledge Requirements

Re-assessment

Re-assessment is not available except when required by referral or deferral.

Notes: See Physics Assessment Conventions.

KIS Data Summary

Miscellaneous