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# Prof. G. S. Iroshnikov

## Quantum mechanics

Курс будет читаться на русском языке!

### Syllabus

### Introduction

Sources of the quantum theory. The main experimental facts. Wave
function and their physical interpretation. Schroedinger equation as a
constraint on the physical state. Feynman's formulation of the quantum
mechanics (path integration) and classical limit.

### The main statements

Quantum mechanics postulates. States and observables, measurable
physical values. Operators, Hermithian operators.

### Mathematical tools

Dirac formalism. State vector. Eigenvalues and eigenfunctions. Unitary
transformation.

### Schroedinger equation

Hamiltonian operator. Time dependent Schroedinger equation. Continuity
equation. Density of probability, flow density. Time dependence of
observables. Commutators, conservation of values.

### One-dimensional movement

Harmonic oscillator, coherent states.

### The angular momentum

Orbital momentum. Spherical harmonics. Parity. Addition of momentums.
Spin and spinors.

### Central forces

Hydrogen atom. Radial equation. Energy spectrum, degeneracy.

### Time independent perturbation theory

Common approach. Case of degeneracy. Hydrogen Stark effect. Spin orbit
interaction. Zeeman effect, permitted and forbidden spectral lines.

### Time dependent perturbation theory

Transitions in discrete and in continuous spectrums. Fermi "golden
rule". Decay of metastable states.
### Emission and absorption of radiation

Quantization of the free electromagnetic field, hamiltonian. Rate of
emission and absorption. Dipole approximation. Selection rules.

### Scattering theory

Amplitude and crossection of scattering. Elastic scattering. Green's
function. Born approximation. Phase theory. Low energy scattering.

### Optic theorem

### References

Landau L.D., Lifshitz E.M. Quantum mechanics.- M.: Nauka, 1974.

Messiah A. Quantum mechanics.-M.: Nauka, Vol.1, 1978, Vol.2, 1979.

Davidov A.S. Quantum mechanics.-M.: Nauka, 1973.

Iroshnikov G.S. Path integral and coherent states in quantum mechanics
and field theory. -M.: MIPT, 1997.

Galitskii V.M. et al. Tasks on quantum mechanics.-M.: Nauka, 1981.