Does adding a proton change the atom's orbital angular momentum? Find the probability that the energy is unchanged.
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):
Not sure how to find this value, without using brute force integration.