ABSTRACT
Consider a quantum mechanical system beginning at a time ti with an eigenstate ψn(x, ti). Suppose its potential is slowly changing. We assume that ∂H/∂t is very small. Then according to adiabatic approximation the wave function ψ of the system is given by
ψ(t) = ∑ n
an(t)ψn(t) e −i ∫ t
where an’s are unknown to be determined, En is the energy eigenvalue of nth state and
∑ runs over all possible states. The phase factor −i ∫ t
ti En(t
′) dt′ is called the dynamical phase. In adiabatic approximation the initial state ψn(ti) changes into ψn(t, ti) without combination with other states. Hence, Eq. (5.1) can be written as
ψ(t) = eiη(t,ti) ψn(t) . (5.2)
Usually, the phase factor η(t, ti) is set to zero as only ψψ∗ is measurable. It has been assumed that η(t, ti) does not give any observable effect.
