
 A free particle, onedimensional wave packets, the Heisenberg uncertainty relations, the
time evolution of a free wave packet, the spreading of a wave packet

 A particle in a timeindependent scalar potential, potential steps, square wells, dfunction potentials

 The WKB approximations for bound states

 Linear vector spaces, Dirac notation, subspaces, linear operators, Hermitian operators,
unitary operators, function of operators, representations in state
space, change of
representation, the eigenvalue problem, commuting observables, the r> and p>
representations

 Postulates, mean value and rootmeansquare deviation, conservation of probability, the
evolution operator

 The Schroedinger picture, the Heisenberg picture, the interaction picture,
timedependent perturbation theory, the evolution of the mean value of an observable,
interference effects

 A statistical mixture of states, the density operator, the physical meaning of the
density matrix and the density operator

 The eigenvalues and eigenfunctions of the 1D harmonic oscillator, the mean value and
root mean square deviation of X and P, coherent states, tensor product spaces, the 3D
harmonic oscillator

 Spin, a spin 1/2 particle in a uniform magnetic field, a general study of a twolevel
system

 The tensor product space of two spin 1/2 particles

 Commutation Relations, basis states, orbital angular momentum, the spherical harmonics

 The translation operator, the rotation operator, rotation of observables, scalar and
vector observables, spinors, the rotation operator for a spin 1/2 particle