Physics 5371

Quantum Mechanics II
Physics 5371 Syllabus

[After J.J. Sakurai, “Modern Quantum Mechanics”, Chs.5-7; J.J. Sakurai, “Advanced Quantum Mechanics”, Chs.2,3.]

Approximation Methods

Time-independent perturbation theory: nondegenerate case
Time-independent perturbation theory: the degenerate case
Hydrogenlike atoms: fine structure and the Zeeman effect
Variational methods
Time-dependent potentials: the interaction picture
Time-dependent perturbation theory
Applications to interactions with the classical radiation field
Energy shift and decay width

Identical Particles

Permutation symmetry
Symmetrization postulate
Two-electron system
The Helium atom
Permutation symmetry and Young Tableaux

Scattering Theory

The Lippmann-Schwinger equation
The Born approximation
Time-dependent formalism: the S-matrix
Optical theorem
Eikonal approximation
Free-particle states: plane waves versus spherical waves
Method of partial waves
Low-energy scattering and bound states
Resonance scattering
Identical particles and scattering
Symmetry considerations in scattering
More time-dependent formalism
Inelastic electron-atom scattering
Nucleon form factors

Quantum Theory of Radiation

Classical radiation field
Creation, annihilation and number operators
Quantized radiation field
Emission and absorption of photons by atoms
Rayleigh scattering, Thompson scattering and the Raman effect
Radiation damping and resonance fluorescence
The Lamb shift

Realtivistic Quantum Mechanics of Spin 1/2 Particles

Probability conservation
The Dirac equation
Simple solutions
The hydrogen atom
Bilinear covariants
Quantization of the Dirac field