# Hydrogen wave function in terms of m_z after m_y measurement

1. Dec 2, 2013

### sapphire_glow

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

Given the following wave function for hydrogen:

psi(r, t=0) = (1/sqrt(10))*(2*psi_100 - psi_210 + sqrt(2)*psi_211 + sqrt(3)*psi_21(-1))

where the subscripts show n, l, m_z, respectively, and the psi_nlm_z are already normalized.

- At t=0, we measure and find l = 1 and m_y = +1. Now what is the normalized wave function immediately after the measurement, in terms of the psi_nlm_z from the original expression? Also, what are the possible values of an energy measurement?

2. Relevant equations

- psi_21(my=+1) = 1/(sqrt(10))*(C1*2*psi_100 - C2*psi_210 + C3*sqrt(2)*psi_211 + C4*sqrt(3)*psi_21(-1))

- Ly |l, z> = (-i/2)*(L+ - L-) |l, z>, with known eigenvalues for L+ and L- (if useful)

3. The attempt at a solution

As shown in relevant equation #1, the result of the measurement must be a linear combination of the original states with mz, as that's all we have to start with (the measurement collapses the original wave function). I'm not really sure what to do next, though... anyone have any pointers? Is it true that the result of m_y = 1 implies that the operator applied here must have been Ly? (hence the second equation tentatively given in part 2)