For 10 points, name this statement originally developed by Born and Fock, which suggests that a slowly evolving system will retain its instantaneous eigenstate throughout an energetic transition
This statement can be used to derive a generalized version of Dykhne's formula that includes a geometric prefactor. A stronger version of this statement is applicable to any piecewise twice-differentiable, finite- dimensional spectral projection. That version was stated by Avron and Elgart, who built on Kato's extension of this statement to discrete, non-degenerate spectra in order to eliminate the gap condition that determines the timescale for its namesake limit. A result of this statement is that avoided crossing occurs when the Landau-Zener velocity is zero. This statement implies the existence of a gauge-invariant phase difference between the initial and final states of a system, when at least two Hamiltonian parameters undergo its namesake type of transport along a closed loop. For 10 points, name this statement originally developed by Born and Fock, which suggests that a slowly evolving system will retain its instantaneous eigenstate throughout an energetic transition
This statement can be used to derive a generalized version of Dykhne's formula that includes a geometric prefactor.
adiabatic theorem [do not accept or prompt on "adiabatic approximation"]