 Solution

ID: past-exam-of-the-options-i-course-of-the-university-of-oxford/2013/j/1/a/solution

i ℏ \partial_{t} Ψ = - \frac{ℏ ^{2}}{2 m} \partial_{x}^{2} Ψ + V (x) Ψ.

E

Ψ (x, t) = ψ (x) e^{- i Et /ℏ}

, where

- \frac{ℏ ^{2}}{2 m} ψ^{''} + V ψ = E ψ .

Its time dependence is only a global phase, and its probability density is independent of time.

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