- #1

dirtyaldante

- 10

- 0

## Homework Statement

1.Determine the expectation value of the potential energy [V(r) = (e^2)/(4.pi.epsilon0.r)] in the 1s (ground state) of the Hydrogen atom.

2.What is the expectation value of r for an electron in the 1s state of the Hydrogen atom?

## Homework Equations

<V(r)> = INT [PSI*|V(r)^|PSI]

n=1, l=0, ml=0

## The Attempt at a Solution

So the method I used to solve other expectation values (<L^2>,<Lz>,<E> etc...) was to use the appropriate operator upon the square of the wavefunction in question, ie: PSI(n,l,ml).

However I can't find operators for the Potential(V(r)) or r(position I suppose) that are related to the quantum numbers n,l and ml like in the other expectation values I solved. e.g.

L^2^=l(l+1)hbar

E^=13.6/n^2

Lz^=ml.hbar

So then I would square the wavefunctions and their coefficients inside the integral and then use the operators appropriately, in this case on the PSI(1,0,0) for the 1s configuration.

Am I simply missing a fundamental operator here? Or do I have to try arrange the operators myself? Rearranging the Schrodinger equation in terms of V(r)PSI was the only thing I could think of and even then I couldn't navigate through the wavefunctions of the separate parts.

Another idea I had was to use the Laguerre polynomial to redefine the wavefunction, but I'm unsure on how to proceed after that.

Is my method just completely off for these expectation values? I have been scratching my head all day over this and would really appreciate help if anyone can offer it.