Quantum mechanics

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.


Rambler's Top100