Introductory description

The principles of quantum mechanics are applied to a range of phenomena in atomic physics including the operation of a laser. The intrinsic property of spin is described and its relation to the indistinguishability of identical particles in quantum mechanics discussed. Perturbation theory and variational methods are described and illustrated for several examples. The hydrogen and helium atoms are analysed and the ideas that come out from this work are used to obtain a qualitative understanding of the periodic table.

Module web page

Module aims

Outline syllabus

This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.

Revision of 2nd year quantum theory

1. Approximation methods in quantum mechanics. Time-independent perturbation theory, non-degenerate case, ground state of helium atom, degenerate case, Stark effect in hydrogen. Variational methods: Rayleigh - Ritz, ground state of helium atom

2. Spin-orbit coupling and the Zeeman effect. Effects of spin-orbit coupling, and the strong and weak field Zeeman effect using time-independent perturbation theory

3. Many electron effects-indistinguishability of identical particles. Identical particles and spin; symmetric and anti-symmetric states; discussion of periodic table, ionisation energies

4. Time-dependent perturbation theory and the lasers. Derivation of Fermi's golden rule; radiation from atoms.; operation of the laser including stimulated emission and population inversion

Learning outcomes

By the end of the module, students should be able to:

• Use the approximate methods of quantum theory – perturbation theory (time-dependent and time-independent), variational methods
• Explain the role of spin and the Pauli exclusion principle
• Explain atomic spectra and the structure of the periodic table
• Describe the operation lasers

Indicative reading list

F Mandl, Quantum Mechanics, Wiley;
A.I.M. Rae, Quantum Mechanics, IOP, 2002;
S. Gasiorowicz, Quantum Physics, Wiley, 2003;
S.M. McMurry, Quantum Mechanics, Addison-Wesley 1994

View reading list on Talis Aspire

Subject specific skills

Knowledge of mathematics and physics. Skills in modelling, reasoning, thinking.

Transferable skills

Analytical, communication, problem-solving, self-study