REVIEW

QUANTUM MECHANICS

Evidence that classical mechanics and classical electricity and magnetism fails in the subatomic domain:

• Black-Body Radiation and Planck's distribution (Reyleigh-Jeans Law, Wien's Law and Stephan's Law; the photon)

• Photoelectric Effect and Einstein's theory (quantization of light)

• Wave nature of electrons: Davison-Germer experiment and de Broglie's formula

Foundations of Quantum Mechanics:

• Postulates of QM, states and wave functions; observables and operators; possible measured values and eigenvalues; average values and <y|A|y>/<y|y>; equation of motion and Schroedinger's equation (stationary state version); indistinguishable particles, spin and permutational symmetry.

• Particle in a box. Solving the Schroedinger equation. Boundary values. Well behaved wave functions. Energy eigenstates, quantum numbers and nodes. Particle in a box in 2 (or 3) dimensions, degeneracy.

• Rigid Rotor in a plane, on a sphere. Shapes of wave functions in three dimensions (angular nodes), directions of maxima. Spherical harmonics in complex and real forms.

• Simple Harmonic Oscillator in one dimension. Tunneling.

• Hydrogen Atom wave functions. Shapes, quantum numbers, nodal surfaces, real forms, quantum numbers. Hydrogen atom energy levels, degeneracy, transitions and selection rules. Electron distribution: angular, radial probability density. Radial distribution: most probable radius (Bohr radius), average radius.

ATOMIC STRUCTURE and ATOMIC SPECTRA

He atom, independent electron approximation, electron configurations, spin and antisymmetry. Spin singlet and triplet wave functions.

Building-up (aufbau) of atomic configurations. Orbital energy ordering, Pauli exclusion. Shells and subshells. Term symbols: coupling angular momenta L, S, and J quantum numbers, 2S+1 multiplicity. Selection rules.