| Outline: |
|
Introduction - The need for Quantum Mechanics
(photoelectric effect, UV catastrophe, Bohr atom, de Broglie
waves, Compton scattering)
Quantum Behavior - Probability and interference,
wave-particle duality, Uncertainty Principle
Schrödinger's Equation - Wave mechanics, particle in a
one-dimensional box, expectation values (energy and
position)
Postulates of Quantum Mechanics - System description,
hermitian operators, wavefunction expansion, measurement,
reduction, time evolution
Operators and Observables - Schrödinger's equation as an
eigenvalue-eigenfunction equation, momentum operator,
space-momentum commutation, free particle wavefunction,
eigenstates of particle in a one-dimensional box
Wave Packets and Momentum Space - Space-momentum
transforms, commutation relations, Gaussian wavepacket,
time evolution, Uncertainty Principle
Square One-Dimensional Potentials - Barrier penetration,
finite square well, attractive (square) potential wells, alpha
decay, delta function potentials (Kronig-Penney model)
Other One-Dimensional Potentials - Momentum space
solution to Schrödinger's equation for triangular potential,
WKB approximation
Dirac Notation - Matrix representation of operators,
commutators and uncertainty relations
Harmonic Oscillator - Solution through Schrödinger's
equation, WKB solution (?), operator method (creation and
annihilation operators)
Approximation Methods for Stationary States -
Time-independent perturbation theory, variational method
Schrödinger's Equation in Two- and Three-Dimensions |