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,