Lecturer: Martin Lees and Ben Green

Weighting: 10 CATS

The principles of quantum mechanics are applied to a range of phenomena in atomic physics including the operation of a laser. The module also covers perturbation theory and variational methods.

Aims:

Objectives:

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 of lasers
• Explain oscillations in two-level systems

Syllabus:

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. Density matrix and Bloch equations.

5. Two-level systems. Examples to include some of the ammonia clock, Rabi oscillations, qubits, magnetic resonance

Commitment: 20 lectures

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

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;