PHYS 5250 - Graduate Quantum Mechanics - I

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Lecture Notes

  • Lecture set 1: Introduction and overview
    • course overview
    • review of Lagrangian, Hamiltonian and Hamilton-Jacobi formulation of classical mechanics
    • conflicts with experiments
    • key ideas in and coordinate formulation of quantum mechanics
  • Lecture set 2: Postulates and mathematical structure of quantum mechanics
    • Hilbert space and Dirac notation
    • physical observables via Hermitian operators
    • Heisenberg uncertainty principle
    • measurement and probabilistic interpretation, density matrix
    • Schrodinger, Heisenberg and Interaction evolution
    • Feynman's path-integral formulation
  • Lecture set 3: Simple applications
    • free particle
    • particle in a box
    • delta-function potential
    • linear potential
    • harmonic oscillator and coherent states
  • Lecture set 4: N-particles quantum mechanics
    • Hilbert space
    • indistinguishable particles and permutation symmetry
    • bosons, fermions and anyons
    • Bose gas
    • Fermi gas
  • Lecture set 5: Symmetries and conservation laws
    • translations
    • rotations
    • time-translations
    • inversion and parity
    • time-reversal
    • gauge "invariance" in quantum mechanics, Aharonov-Bohm effect, and Berry topological phase
  • Lecture set 6:Orbital angular momentum
    • general formulation
    • representation theory of SO(3) rotations
  • Lecture set 7: Rotationally invariant problems
    • free particle
    • isotropic harmonic oscillator
    • electron in a magnetic field -- Landau levels
    • Hydrogen atom
  • Lecture set 8: Spin and total angular momentum
    • SU(2) spinor representation
    • addition of angular momenta
    • Zeeman Hamiltonian and splitting
    • spin from Dirac equation
    • spin precession and NMR
    • spin-orbit interaction

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