# PX382 Quantum Physics of Atoms

## Lecturer: Martin Lees

## Weighting: 7.5 CATS

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 applied to several problems. The hydrogen and helium atoms are analysed and the ideas that come out from this work are used to obtain a good qualitative understanding of the periodic table.

**Aims:**

To develop the ideas of quantum theory and apply these to atomic physics

**Objectives:**

At the end of the module you should:

- Have developed an understanding of the approximate methods of quantum theory – perturbation theory (time-dependent and time-independent), variational methods
- Understand the role of spin and the Pauli exclusion principle
- Be able to explain atomic spectra and the structure of the periodic table
- Have an understanding of lasers

**Syllabus:**

**Review of Second Year Quantum Mechanics
**

**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.

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

**Spin-orbit coupling and the Zeeman effect**

**Many electron effects-indistinguishability of identical particles**Identical particles and spin.

Symmetric and anti-symmetric states.

Discussion of periodic table, ionisation energies.

**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.

**Commitment:** 15 lectures

**Assessment:** 1.5 hour examination (85%) + assessed work (15%).

This module has a home page.

**Recommended Texts:** S.M. McMurry, *Quantum Mechanics*, Addison-Wesley 1994

F Mandl, *Quantum Mechanics*, Wiley A.I.M. Rae, *Quantum Mechanics*, IOP, 2002; S. Gasiorowicz, *Quantum Physics*, Wiley, 2003;

**Leads from:** PX262 Quantum Mechanics and its Applications;

**Leads to**: Other modules on quantum theory and quantum phenomena.