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I am having trouble with 2 problems about the harmonic oscilator.

First of all the question tells me to use the wave function for when n=1

So I have:

Wavefunction = A[1]*r^1/2 * x * e^-((r^2)/2)

where r= (mw/(hbar))^1/2

I am wondering when I am multiplying this by the complex conjugate, is the complex conjugate going to have a e^+((r^2)/2). I dont think I am but for some reason, in a solution finding <x> which equals ](integral) psi* (times) x (times) psi] those exponential functions did not appear. So I was wondering how they cancelled out when you calculate <x>

also it asks me to calculate <p>, which I know equals m*d<x>/dt. My question is, if my <x> does not depend on t, because the time dependent part of the equation was cancelled out when solving for <x>, how can I find d<x>/dt?

Any help would be appreciated, I'm sure my questions or equations aren't too clear, so if you have any questions, I will try to clarify. Thank you.

First of all the question tells me to use the wave function for when n=1

So I have:

Wavefunction = A[1]*r^1/2 * x * e^-((r^2)/2)

where r= (mw/(hbar))^1/2

I am wondering when I am multiplying this by the complex conjugate, is the complex conjugate going to have a e^+((r^2)/2). I dont think I am but for some reason, in a solution finding <x> which equals ](integral) psi* (times) x (times) psi] those exponential functions did not appear. So I was wondering how they cancelled out when you calculate <x>

also it asks me to calculate <p>, which I know equals m*d<x>/dt. My question is, if my <x> does not depend on t, because the time dependent part of the equation was cancelled out when solving for <x>, how can I find d<x>/dt?

Any help would be appreciated, I'm sure my questions or equations aren't too clear, so if you have any questions, I will try to clarify. Thank you.

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