640-344 Quantum Systems

Credit Points:

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Objectives:

By the end of this course students should:

• comprehend how quantum mechanics is used to understand the structure of matter;

• appreciate that the existence and behaviour of atoms and molecules are inexplicable unless quantum mechanics is used;

• be able to apply quantum mechanics to answer some important questions about quantum systems.

Content:

Aspects of the following topics will be considered:

Systems of N identical particles; symmetrisation and antisymmetrisation; bosons and fermions; spin-statistics relation; Pauli Exclusion Principle; applications.

Helium atom, perturbative and variational approaches; atomic degeneracy; perturbation theory for degenerate levels; introduction to many-electron atoms; angular momentum; fine and hyperfine structure.

Atoms in static electromagnetic fields; Stark effect; Zeeman effect, magnetism.

Introduction to molecules and chemical bonds; Hydrogen Molecular Ion molecule; Born-Oppenheimer approximation; energy levels of molecules.

Time-dependent perturbation theory; electromagnetic transitions in atoms; Golden Rule; spectroscopy, lasers. Exponential decay, barrier penetration.

Introduction to multiple and periodic potentials and solid state systems; band structure; conductors, insulators, semiconductors.

Assessment:

Prescribed Texts:

• Bransden B H and Joachain C J, Physics of Atoms and Molecules, 1983 Longman.