Quantum physics III

1. Transition from quantum physics to classical mechanics: the coherent
states and the Ehrenfest theorem.

 

2. Semiclassical approximation in quantum mechanics:  general form of
the semiclassical wave function and matching conditions at turning
points.

 

3. One-dimensional problems in semiclassical approximation:
Bohr-Sommerfeld quantisation condition and the Planck formula,
tunnelling probability through a potential barrier, lifetime of a
metastable state, splitting of the energy levels in a double-well
potential.

 

4. Path integral representation of quantum mechanics: Schrodinger
equation from path integral, physical interpretation of the path
integral and the principle of minimal action, Euclidean path integral
and statistical physics, "instanton" and "bounce".

 

5. Scattering theory: cross-section,  Moller operators and S-matrix,
Green's functions and the scattering amplitude, the T-matrix and the
Lippmann-Schwinger formula, perturbation theory for amplitudes and the
Born approximation, scattering amplitude via stationary scattering
states.

 

6.  Relativistic quantum mechanics:  the Dirac equation and its
non-relativistic limit - the  Pauli equation.