Introduction.
Lecture 1.
Equation for the Green function and the path integral.
Hamiltonian and Langrangian.
Linear oscillator. Classical Limit.
Lecture 2.
Particlle in a Box. "Cucumber" problem
Lecture 3
WKB approximation. Over-barrier Reflections
Lecture 4
Semiclassical Green's Function. Over-Barrier Reflection.
Lecture 5.
Density Matrix and Green Function. Energy
Levels and Eigenfunctions.
Over Barrier Reflection. Instanton
Lecture 6.
Relativistic Quantum Mechanics. Dirac Equation.
Non-relativistic Limit.
Pauli Equation. Pair Creation in Electric Field.
Lecture 7.
Path Integral on a Compact Manyfold. Rotor. Hydrogen Atom
Lecture 8.
Adiabatic Approximation. Rotation of Diatomic Molecules
Berry Phase
Lecture 9.
Scattering Problem. Perturbation Theory. Born Approximation.
Lecture 10.
Three-Particles-Scattering. Faddeev Equation
Lecture 11 .
A particle, interacting with a quantized field. Polaron.
Lecture 12.
Quantum Dynamics and its Classical Limit.
Feynmann-Vernon and Keldysh Theories
Lecture 13.
Tunneling a particle, interacted with an environment.
Caldeira-Leggett Theory
Lecture 14.
A particle, interacting with a classical gauge filed.
Infra-red catastrophe. Phase Breaking Rate.
Lecture 15.
Geometric Quantization. Path Integral for a Spin. Statistics. Statistical transmutation
Lecture 16.
Path Integral for Fermions. Fermionic Oscillator. Supersymmetry
Lecture 17.
Broadening of the lowest Landau Level
Lecture 18.
Light adsorbtion. Urbach rule
Lecture 19.
Electron in One-dimensional Random Potential. Anderson Localization.
Lecture 20 .
Weak Disorder and Non-linear sigma-model. Weak Localisation. Dysonian Statistics.
Lecture 21.
Extra-electron in a Superconductor. Shapoval-de Gennes method
Lecture 22.
Strings
Epiloge.
Further Development
Appendix 1
One-dimensional Classical Statistical Mechanics
and
Quantum Mechanics of a Particle. Correlation functions.
Appendix 2
Random Walk with Random Traps
Appendix 3
Sinai Diffusion
Appendix 4
LECTURE NOTES