# Modern Physics and Quantum Mechanics

### Fundamental assumptions of QM, postulates

Formulas

Photons,
DeBroglie wavelength, electron diffraction

The Bohr atom,
nuclei and particles

The
uncertainty principle

Commuting and non-commuting observables

Eigenvalues and
eigenfunctions

Eigenvalues
and Boltzmann statistics

The
Schroedinger equation

Probability
density and the mean value of an observable

The rms deviation

Evolution
of probabilities

Mathematical
foundations

Wave
packets and the Fourier transform

### One-dimensional eigenvalue problems

Formulas

Square potentials, bound states

Square potentials, continuum states

Infinite
wells

Delta
function potentials

Harmonic potentials, eigenvalues and eigenfunctions

Harmonic potentials, raising and lowering operators

Other 1D
potentials

### Angular momentum and spin

Formulas

Orbital angular
momentum

A single spin ½
particle

Two spin ½
particles

Properties of
angular momentum operators

Addition of angular
momentum

### Three-dimensional eigenvalue problems

Formulas

Square
potentials (cube and sphere)

The
hydrogen atom (energy levels and wave functions)

Hydrogenic atoms

The rigid rotator

Other
systems

### Approximation methods (time-independent)

Formulas

The variational method

Perturbation theory, non-degenerate states (harmonic oscillator, atoms)

Perturbation theory, non-degenerate states (other systems)

Perturbation theory, degenerate states

The WKB
method

Mixed
method problems

### Approximation methods (time dependent)

Formulas

Sudden approximation

Time-dependent perturbation theory

Fermi's
golden rule

Mixed
method problems

### Scattering

Formulas

The partial wave method

The Born approximation

Other scattering problems

### Identical particles

Formulas

Counting
statistics

Multi-electron atoms

Symmetry requirements for identical particles

Other problems
involving identical particles