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Дата изменения: Fri Dec 9 17:01:06 2005
Дата индексирования: Tue Oct 2 03:44:00 2012
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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.
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.
