H ^ | Ψ ⟩ = E | Ψ ⟩ {\displaystyle {\hat {H}}\left|\Psi \right\rangle =E\left|\Psi \right\rangle } E wird nach dem Korrespondenzprinzip zu i ℏ ∂ t {\displaystyle i\hbar {{\partial }_{t}}}
( − ℏ 2 2 m Δ + V ^ ) | Ψ ⟩ = i ℏ ∂ t | Ψ ⟩ {\displaystyle \left(-{\frac {{\hbar }^{2}}{2m}}\Delta +{\hat {V}}\right)\left|\Psi \right\rangle =i\hbar {{\partial }_{t}}\left|\Psi \right\rangle }