| Outline: |
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Postulates of Quantum Mechanics [a review using Dirac
notation] - System description (Schrödinger's equation;
eigenvalues and eigenfunctions), hermitian operators (and
observables), wavefunction expansion, measurement
(expectation values, uncertainty relations and commutators),
reduction, time evolution
Schrödinger's Equation in 3-Dimensions - Coordinate
representations for 3-D wave mechanics, particle in a 2- and
3-D box (degeneracy), 2-D harmonic oscillator, two particle
systems (separation, reduced mass), the exchange operator
and identical particles (fermions and bosons)
Orbital Angular Momentum - Introduction to the angular
momentum operator (particle on a ring),
angular-momentum/angle uncertainty relation, the cylinder
potential, angular momentum eigenvalues, the vector model,
spherical harmonics, the operator method, angular
momentum matrix operators
Central Potentials - The Hamiltonian in spherical
coordinates, the spherical box, the spherical square well
(deuteron), the linear potential
The Hydrogen Atom - Eigenvalues of the Coulomb potential
(E < 0), radial eigenfunctions (Laguerre polynomials),
complete spherical wavefunctions
Stark and Zeeman Effects - The Stark effect and electric
polarizability (non-degenerate and degenerate perturbation
theory), electrons in a magnetic field (normal Zeeman effect,
etc.)
Spin States and Matrix Operators - The Stern-Gerlach
experiment, spin matrix mechanics (spinors, Pauli matrices,
the transformation matrix), addition of orbital and spin
angular momentum (Pauli Principle, spectroscopic notation,
etc.)
Time-Dependent Perturbation Theory - General formalism,
periodic perturbation (Fermi's Golden Rule), transitions in
atoms (the dipole approximation and selection rules)
Scattering Theory - Scattering amplitude, cross sections,
Born approximation, partial wave expansion, applications
(e.g. Rutherford scattering)
Other Applications of Quantum Mechanics [if time permits!] -
the ammonia molecule (two-state matrix mechanics), masers
and lasers, fine structure of hydrogen, helium, SQUIDs |