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 qualitative understanding of the periodic table.
To develop the ideas of quantum theory and apply these to atomic physics
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
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.
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.
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%).
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