A topic within Quantum Mechanics, itself one of 12 topics in that field and part of Physics.
3 works
Tosio Kato
Gives the first mathematically rigorous proof that a quantum system changed slowly enough stays in its instantaneous eigenstate, putting the adiabatic approximation used throughout perturbation theory on firm ground.
Notes on this copyJ. E. Avron & A. Elgart
Proves the quantum adiabatic theorem holds even when the spectral gap the classical 1950 statement requires closes, extending Kato's rigorous result to systems with only a piecewise-differentiable spectral projection.
link checked 17 Sept 2026Notes on this copyBarton Zwiebach (MIT OpenCourseWare)
Develops time-independent and time-dependent perturbation theory, the WKB approximation and scattering as the tools for handling the quantum systems that have no exact solution.
link checked 17 Sept 2026Notes on this copy