So, this has been bothering me for a while.(adsbygoogle = window.adsbygoogle || []).push({});

Lets say we have the wavefunction of a harmonic oscillator as a general superposition of energy eigenstates:

[itex]\Psi = \sum c_{n} \psi _{n} exp(i(E_{n}-E_{m})t/h)[/itex]

Is it true in this case that <V> =(1/2) <E> .

I tried calculating this but i get something like

<V> = < [itex]\Psi |V| \Psi [/itex] > = (1/2)<E> + some other term that does not seem to be zero generally.

However, it seems to me that <V> =(1/2) <E> should be true even in this case, since

[itex] <V>_{n} = <\psi_{n} | V | \psi_{n} > = (1/2) <E> [/itex] for every n.

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# Expectation values of harmonic oscillator in general state

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