Here I share my notes on quantum mechanics which I learned in graduate and undergraduate courses. please report any errors found to me.

The primary sources are

  • Sakurai, Jun John, and Jim Napolitano. Modern Quantum Mechanics. 3rd ed, Cambridge University Press, 2021.
  • Griffiths, David J., and Darrell F. Schroeter. Introduction to Quantum Mechanics. Third edition, Cambridge University Press, 2018.
Chapter Section Subsections
1 Fundamental concepts The Stern-Gerlach experiment, Kets, bras, and operators, Base kets and matrix representation, Measurements, observables, and uncertainty relations, Change of basis, Position, Momentum, and Translation, Wave Functions in position and momentum space
2 Quantum dynamics Time evolution and the Schrodinger equation, The Schrodinger versus the Heisenberg picture, Simple harmonic oscillator, Schrodinger’s wave equation, WKB semiclassical approximation, Propagators and Feynman path integrals, Potentials and addictive phase, Gauge transformations in Electromagnetism, Aharanov-Bohm effect, Magnetic monopole
4 Symmetries Symmetry in classical physics, Symmetry in quantum physics, Symmetry and degeneracy, Discrete symmetries: Parity, Discrete symmetries: Lattice translation, Back to the symmetry operators, Discrete symmetries: Time reversal
Part 1 of 5 Approximation methods in time-independent systems Time-independent perturbation theory: The degenerate/non-degenerate cases, variational methods
Part 2 of 5 Exact and approximation methods in time-dependent systems Quantum time evolution pictures: Schrodinger/Heisenberg/Dirac, Extreme time dependence cases: Sudden/adiabatic approximation, Time-dependent perturbation theory
6 Scattering Theory Constant step time-dependent potential, Scattering from constant step time-dependent potential: Born approximation, Plane waves versus spherical waves, Scattering from constant step time-dependent potential with spherical symmetry: Scattering from hard sphere