Project SherlockEst. Knowledge

Paper

1950

On the Adiabatic Theorem of Quantum Mechanics

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.

No free copy is linked yet — expect to buy or borrow this one elsewhere.

Groundwork for

Works in the library that name this one as a prerequisite.

An Adiabatic Theorem without a Gap ConditionJ. E. Avron & A. Elgart, 1998Proves 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.

Filed under Quantum Mechanics in Physics.