G.S.Iroshnikov
Quantum mechanics
 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, Hermitian 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.
 Onedimensional 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.