ADVANCED QUANTUM MECHANICS

Schroedinger equation in the continuum

Elastic diffusion of two particles, scattering amplitude, Born approximation with Coulomb and Yukawa potentials, scattering from an extended target.

Approximation methods for stationary states

Perturbative expansion of the Schroedinger equation in the non degenerate and degenerate cases – Stark effect – Zeeman effect-Variational method – binding energy of the He atom: comparison between perturbative and variational estimates of the binding energy.

Equations of motion

Heisenberg representation – Relation between symmetries and conservation theorems - Classical limit: Ehrenfest theorem- Spreading of the wave packet – two-level system: Rabi formula.

Time dependent perturbation theory

Interaction representation - e.m. atomic quantum transitions – dipole approximation and angular momentum selection rules.

More on the angular momentum

Composition of angular momenta - Clebsch-Gordan coefficients – tensor operators – Wigner-Eckart and projection theorems.

Quantum Statistical Mechanics

Time and statistical average –microcanonical and grancanonical Ensembles – connection with thermodynamics – non interacting fermion and boson gases – black body radiation.

Covariant formulation of the Schroedinger equation

Klein-Gordon equation – Dirac equation and spinors – spin-orbit interaction .

J.J. Sakurai - Advanced quantum mechanics

J.D Bjorken and S. Drell - relativistic quantum mechanics