I'm given that there is a harmonic oscillator in a state that is a superposition of the ground and first excited stationary states given by [tex]\psi = \frac{1}{\sqrt{2}}\abs{\psi_0(x,t) + \psi_1(x,t)}[/tex], where [tex]\psi_0 = \psi_0(x)e^{\frac{-iE_0t}{\hbar}}[/tex] and [tex]\psi_1 = \psi_1(x)e^{\frac{-iE_1t}{\hbar}}[/tex]. I need to calculate expectation values for position, momentum, and total energy.(adsbygoogle = window.adsbygoogle || []).push({});

Here's what I've done: I'm assuming this is a simple harmonic oscillator, and for the x operator I have [tex]\frac{i}{\sqrt{2m\omega}}(a_- - a_+)[/tex]. I think that a- operating on Psi0 would be zero, and on Psi1 would be Psi0, and a+ operating on Psi0 would be Psi1, and on Psi1 would be Psi2. So... I have for <x>:

[tex] <x> = \frac{i}{2\sqrt{2m\omega}}<\psi_0 + \psi_1 | \psi_0 - \psi_1 - \psi_2>[/tex].. but.. uh.. how do you do this? I feel like I must have done something wrong. A push in the right direction would be much appreciated.

Thanks so much!

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# Homework Help: Harmonic oscillator expectation values

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