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.
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.
