# Difficult problem dealing with stationary states of hyrdrogen

Really confused by this one.

## Homework Statement

I'm given that a tritium atom, with one proton and two neutrons in the nucleus, decays by beta emission to a helium isotope with two protons and one neutron in the nucleus. During the decay, the atom changes from hydrogen to singly-ionized helium so Z doubles.

I need to find the probabilities that the helium atom is in the ground state or the first excited state (2s) immediately after the decay; I'm given that the tritium was in the 1s ground state before the decay.

I'm also told to ignore spin.

## Homework Equations

I'm given that since I need to calculate the constants multiplying the eigenfunctions of helium (see below), that I need to use $$<\psi_{n'l'm'}|\psi_{nlm}> = \delta_{n'n}\delta_{l'l}\delta_{m'm}$$ to do that.

## The Attempt at a Solution

Well, to solve it, I need to write the ground state of tritium as a superposition of stationary states of He+, because the square of the absolute value of the constant multiplying a particular helium eigenfunction gives the probability that the helium atom is in that state after the decay.

The trouble is I don't know what the stationary states of He+ would look like.

dextercioby
Homework Helper
He+ is hydrogenoid ion, so the stationary states are computed in QM books when dealing with the Kepler problem for the Coulomb potential.

Daniel.

Hm.. There's no section about that in my QM book, and we haven't mentioned any of the terms you used in class. We've discussed a little bit about hydrogen atoms.. I think I'm supposed to use perturbation theory to find them.. but it's hard when I have no examples or any instruction about it =/

dextercioby