Modern Physics and Quantum Mechanics

Fundamental assumptions of QM, postulates

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

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

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

Square potentials (cube and sphere)
The hydrogen atom (energy levels and wave functions)
Hydrogenic atoms
The rigid rotator
Other systems

Approximation methods (time-independent)

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)

Sudden approximation
Time-dependent perturbation theory
Fermi's golden rule
Mixed method problems


The partial wave method
The Born approximation
Other scattering problems

Identical particles

Counting statistics
Multi-electron atoms
Symmetry requirements for identical particles
Other problems involving identical particles