Quantum Mechanics (PHY 312)

Course description

Angular momentum and symmetries in quantum mechanics from group theory viewpoint; time-independent and time-dependent perturbation theory; path integral formulation; scattering theory; identical particles; applications.

Possible principal texts:

  1. Cohen-Tannoudji, Diu and Laloe, Quantum Mechanics - 2 vols. (Wiley-Interscience)
  2. Shankar, Principles of Quantum Mechanics (Springer)
  3. Greiner, Müller, Quantum Mechanics: Symmetries (Springer)

Other texts to consider:

  1. Sakurai, Modern Quantum Mechanics (Addison-Wesley)
  2. Merzbacher, Quantum Mechanics (Wiley, 3rd edition)

Prerequisites

The prerequisite is at least one semester of a Quantum Mechanics course at the level of R. Shankar's textbook.

In Duke Physics, there is an undergraduate "Quantum Mechanics I" course (PHY 211), with the synopsis:

Experimental foundation of quantum mechanics; wave-particle duality; the single-particle Schrodinger equation and the physical meaning of the wave function; methods for studying the single-particle Schrodinger equation; analytical solutions of the harmonic oscillator and hydrogen atom and experimental tests of these solutions; angular momentum and spin systems; and finally the many-particle Schrodinger equation and consequences of identical particles existing in nature.

Syllabus

  • Time-independent perturbation theory.
  • The “real” hydrogen atom.
  • Identical particles, exchange interaction, helium atom.
  • Many-body states, Slater determinant, Hartree-Fock approximation.
  • Variational method: hydrogen molecule, chemical binding.
  • Periodic potential, Bloch waves, band structure.
  • Time-dependent perturbation theory, Fermi’s Golden Rule.
  • Application to two-state system (e.g., spin rotations, NMR).
  • Elementary two-state systems: neutral kaons or neutrino oscillations.
  • Continuous symmetries, Noether’s theorem, rotation group SO(3).
  • Addition of angular momenta, Clebsch-Gordon coefficients.
  • Tensor operators, Wigner-Eckart theorem.
  • SU(2) and its relationship to SO(3), isospin (weak & strong).
  • Path integral formulation of QM: Principles, free particle, semiclassical limit, particle on a circle, Berry’s phase.
  • WKB approximation.
  • Scattering theory: cross section, S-matrix, T-matrix, unitarity, Born approximation, partial waves, optical theorem.
Choice of special topics: quantum information theory, renormalization group, etc.

There is a sample course description.

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