The time dependent Schrödinger equation is
|
−{{ℏ}^{2}\over
2m} {{∂}^{2}\over
∂{x}^{2}}ψ(x,t) + V (x)ψ(x,t) = {ℏi∂\over
∂t} ψ(x,t).
| (10.1) |
As we remember, a solution of the form
|
ψ(x,t) = ϕ(x){e}^{−iEt∕ℏ}
| (10.2) |
leads to a solution of the time-independent Schrödinger equation of the form
|
−{{ℏ}^{2}\over
2m} {{∂}^{2}\over
∂{x}^{2}}ϕ(x) + V (x)ϕ(x) = Eϕ(x).
| (10.3) |