- #1

- 1,728

- 13

## Homework Statement

Does adding a proton change the atom's orbital angular momentum? Find the probability that the energy is unchanged.

## Homework Equations

## The Attempt at a Solution

The orbital angular momentum is unchanged, since ##<L^2> = l(l+1)\hbar^2## is independent of Z.

To find the probability that the energy is unchanged, we overlap the old state (Z=1) with the new state (Z=2):

[tex]|\langle\psi^{Z=1}|\psi^{Z=2}\rangle[/tex]

Not sure how to find this value, without using brute force integration.