How can the virial theorem be applied to a quantum particle in one dimension?

[subny]

Homework Statement

A quantum particle, i.e. a particle obeying Schrodinger equation and
moving in one dimension experiences a potential ˆV (x). In a stationary state
of this system show that

⟨x∂/∂x(ˆV(x)⟩ = ⟨ˆp2/2m⟩

Hint: Consider the time dependence of ⟨ˆxˆp⟩.

Homework Equations

I was told the answer would be some variation of the virial theorem as proven here - http://www7b.biglobe.ne.jp/~kcy05t/viriproof.html#qua

but i do not get the connection

The Attempt at a Solution

I was thinking of doing it as per the hint - by trying to find the d/dt of <^x^p>

(something prefixed by a "^" signifies an operator - i.e "^p" is the momentum operator etc

 

[andrien]

just go with d/dt<x.p> and prove that <x.p> for stationary state is independent of time.Use the formula from the reference you already have for d/dt<O>,where O is some operator.
EDIT-wait,does not that reference already has solution.

 

[subny]

hi

so i am confused now - does the reference already have the soln - i don't even see it !

 

[subny]

hmm... any other hints or suggestions.

Thanks

 

[andrien]

All right,see this one
https://www.physicsforums.com/showthread.php?t=667817