Physics 5370

Quantum Mechanics I
Physics 5370 Syllabus

[After J.J. Sakurai, “Modern Quantum Mechanics”, Chs.1-4.]

Fundamental Concepts

  • The Stern-Gerlach experiment
  • Kets, bras and operators
  • Base kets and matrix representations
  • Measurements, observables and uncertainty relations
  • Change of basis
  • Position, momentum and translation
  • Wave functions in position and momentum space

Quantum Dynamics

  • Time Evolution and the Schrodinger equation
  • The Schrodinger versus the Heisenberg picture
  • Simple Harmonic Oscillator
  • Schrodinger’s wave equation
  • Propagators and Feynman path integrals
  • Potentials and gauge transformations
  • Magnetic monopoles

Theory of Angular Momentum

  • Rotations and angular momentum commutation relations
  • Spin 1/2 systems and finite rotations
  • O(3), SU(2) and Euler rotations
  • Density operators and pure versus mixed ensembles
  • Eigenvalues and eigenstates of angular momentum
  • Orbital angular momentum
  • Addition of angular momenta
  • Tensor operators

Symmetry in Quantum Mechanics

  • Symmetries, conservation laws and degeneracies
  • Discrete symmetries, parity, or space inversion
  • Lattice translation as a discrete symmetry
  • The time-reversal discrete symmetry