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Find the time dependance of the expectation value <x> in a quantum harmonic oscillator, where the potential is given by [tex] V=\frac{1}{2}kx^2 [/tex]

I'm assuming some wavefunction of the form [itex] \Psi(x,t)=\psi(x) e^{-iEt/\hbar}[/itex]

When I apply the position operator, I get:

[tex] <x>=\int_{-\infty}^\infty {\psi_0}^2 (x) e^{\-iEt/\hbar}e^{iEt/\hbar}dx [/tex]

[tex] <x>=\int_{-\infty}^\infty {\psi_0}^2 (x) [/tex]

which is time-independent, and also wrong...

I think it's supposed to be an easy question, and I'm supposed to get the classical result, i.e. [itex] x=x_0 cos(2\pi\nu t+\phi) [/itex]Some help would be much appreciated.

I'm assuming some wavefunction of the form [itex] \Psi(x,t)=\psi(x) e^{-iEt/\hbar}[/itex]

When I apply the position operator, I get:

[tex] <x>=\int_{-\infty}^\infty {\psi_0}^2 (x) e^{\-iEt/\hbar}e^{iEt/\hbar}dx [/tex]

[tex] <x>=\int_{-\infty}^\infty {\psi_0}^2 (x) [/tex]

which is time-independent, and also wrong...

I think it's supposed to be an easy question, and I'm supposed to get the classical result, i.e. [itex] x=x_0 cos(2\pi\nu t+\phi) [/itex]Some help would be much appreciated.

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