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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

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.