Adiabatic switching methods for calculating eigenstates.

The adiabatic theorem in quantum mechanics states that if is an eigenfunction sufficiently of H(0), and H(t) is a slowly varying function of time, then will evolve in such a way as to remain an eigenfunction of H(t) for all time. This property may be exploited to calculate eigenfunctions for complicated potentials, V, by starting in an eigenfunction of a simple potential and slowly "switching" on the difference potential, where varies slowly from 0 to 1. In the example below, is chosen as the harmonic oscillator potential, and V is the double well potential,

The adiabatic theorem in quantum mechanics states that if is an eigenfunction sufficiently of H(0), and H(t) is a slowly varying function of time, then will evolve in such a way as to remain an eigenfunction of H(t) for all time. This property may be exploited to calculate eigenfunctions for complicated potentials, V, by starting in an eigenfunction of a simple potential and slowly "switching" on the difference potential, where varies slowly from 0 to 1. In the example below, is chosen as the harmonic oscillator potential, and V is the double well potential,