10.1 correspondence between time-dependent and time-independent solutions

The time dependent Schrödinger equation is

−ℏ22m∂2∂x2ψ(xt)+V(x)ψ(xt)=∂tℏi∂ψ(xt)

(10.1)

As we remember, a solution of the form

ψ(xt)=ϕ(x)e−iEt∕ℏ

(10.2)

leads to a solution of the time-independent Schrödinger equation of the form

−ℏ22m∂2∂x2ϕ(x)+V(x)ϕ(x)=Eϕ(x)

(10.3)