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Normalize Harmonic Oscillator wave functions

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The following are two harmonic oscillator wave functions:

S(x) = N exp(-max/2h)(2mwx/h)
S(x) = N exp(-max/2h)[8(mwx/h)^3 - 12mwx/h]

where N = .

Show that they are a) normalized, and b) orthogonal

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I have shown how to find if two harmonic oscillator wave functions are orthogonal. Also, I have shown how to find if the are normalized.

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Note to student: Please find the answer in the attached file. All these problems involved the integration of one type of standard integral. ...

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