Axioms for QM [Eigenvalues, simultaneous
Eigenvectors, Eigen-bases, scalar products and ortho-normality relations,
diagonalisation, differential and matrix operators, commutation relations,
stationary states, superposition and Fourier analysis, completeness relations,
the Hamiltonian and unitary evolution, probability amplitudes and physical
interpretations].
1D Schrodinger equation for a spinless particle in
potential V(x) [Simple Harmonic Oscillator (SHO), Hermite Functions, Zero-Point
Energy, Coherent states, notions of resonance in wells and transmission and
reflection coefficients, concept of orbital parity and reflection symmetry].
3D Schrodinger equation for spinless particle in
potential V(x,y,z) [3D SHO, degeneracy, Barrier penetration and α decay].
Rotations and Angular Momentum [Commutation
Relations for Orbital operators Lx,Ly,Lz,L2,
simultaneous eigenfunctions, Schrodinger representation in Cartesian and Spherical
Polar Coordinates, angular Laplacian, and Spherical harmonics].
3D Central Potentials V(r) [Spherical Polar
Formulation, Coulomb potential, bound states, the H atom without electron
spin].
Electron Spin [Pauli matrices and complex 2D
spinors, the Pauli-Schrodinger equation, magnetic moment of the electron, the
H atom with electron spin].
Addition of Angular Momentum [Clebsch-Gordan
techniques].
Interaction of magnetic moment with static magnetic
field [Spin precession and magnetic resonance, intrinsic nucleon spin].
Several
electron atoms [Identical Particles, Bosons and Fermions, atomic structure and
the periodic table, the electron-electron interaction].
Approximation Methods [Time-independent
Rayleigh-Schrodinger Perturbation theory, non-degenerate perturbation theory,
degenerate perturbation theory, variational methods and WKB, Zeeman and Stark
effects, H atom in weak (strong) magnetic (electric) field, periodic potentials
and band structure, paramagnetism].
Time Dependent Interactions [The Heisenberg Picture
and time dependent Hamiltonians, time dependent perturbation theory,
first-order transitions, transition into a continuous spectrum and the
Fermi-Golden rule, periodic perturbations, the radiation field and selection
rules for electric dipole transitions, Hamiltonian for emission and absorption
of photons, spontaneous emission and the Einstein coefficients, applications to
lasers].
