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Shredface
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Homework Statement
Suppose you assume that you have normalised a wave function at t = 0. How do you know that it will stay normalised as time goes on? Show explicitly that the Schrodinger equation has the property that it preserves normalistion over time.
Homework Equations
From my notes I have deduced:
[tex]\frac{d}{dt} \int_{-\infty}^{+\infty} \left| \Psi\left(x,t\right)\right|^2 dx = \int_{-\infty}^{+\infty} \frac{\partial}{\partial t} \left| \Psi\left(x,t\right)\right|^2 dx = 0[/tex]
However I have failed to come up with a solution.
EDIT: Should I rearrange the Schrodinger equation for d/dt of psi then solve that way? I'm confused.
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