# Homework Help: Virial theorem, hamiltonian

1. Apr 17, 2013

### subny

1. The problem statement, all variables and given/known data
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⟩.

2. Relevant 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

3. 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

2. Apr 18, 2013

### 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.

Last edited: Apr 18, 2013
3. Apr 18, 2013

### subny

hi

so i am confused now - does the reference already have the soln - i dont even see it !!

4. Apr 18, 2013

### subny

hmm... any other hints or suggestions.

Thanks

5. Apr 20, 2013