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I want to show that

[tex] \frac{d}{dt} \int_{-\infty}^{\infty} \psi_1^{*}\psi_2 dx = 0 [/tex]

for any two (normalizable) solutions to the Schrödinger equation. I have tried rearranging the Schrödinger equation to yield expressions for [tex] \psi_1^{*} [/tex] and [tex] \psi_2 [/tex] like this:

[tex] \psi_1^{*} = \frac1{V(x)}\left( ih\frac{\partial \psi_1^{*}}{\partial t} + \frac{h^2}{2m}\frac{\partial^2 \psi_1^{*}}{\partial x^2} \right) [/tex]

[tex] \psi_2 = \frac1{V(x)}\left( ih\frac{\partial \psi_2}{\partial t} + \frac{h^2}{2m}\frac{\partial^2 \psi_2}{\partial x^2} \right) [/tex]

It gets me nowhere...

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# Qm problem

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