Hi everyone(adsbygoogle = window.adsbygoogle || []).push({});

I have a question regarding a step in the proof of the Virial Theorem.

Specifically suppose [itex]|E\rangle[/itex] is a stationary state with energy [itex]E[/itex], i.e.

[tex]\hat{H}|E\rangle = E|E\rangle[/tex]

Now,

[tex][\hat{r}\bullet\hat{p},\hat{H}] = i\hbar\left(\frac{p^2}{m} - \vec{r}\bullet\nabla V\right)[/tex]

Taking the expectation value of the left hand side over stationary states, we see that

[tex]\langle E|[\hat{r}\bullet\hat{p},\hat{H}]|E\rangle = 0[/tex]

(The Virial Theorem for central potentials then assumes [itex]V(r) = \alpha r^{n}[/itex] and one gets <T> = (n/2)<V>.)

My question is:what is the physical significance of this commutator and what does it mean physically that the expectation of this commutator wrt a basis of stationary states is zero?

Thanks in advance.

Cheers,

Vivek.

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# Virial Theorem

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