# Set of Commuting Observables for pures states 2p-1,2px and 2s

1. Nov 12, 2013

### DielsAlder

Hi,

Here I have a question, apparently easy, but that I think it is a bit tricky.

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

Indicate how can a hydrogen atom be prepared in the pure
states corresponding to the state vectors ψ2p-1 and ψ2px and
ψ2s. It is assumed that spin-related observables are not
relevant.

Hint: The state ψ2px becomes the state ψ2pz = ψ2p0 by a rotation
of 90º of the cartesian axis system

2. Relevant equations

Just remind the Hamiltonian H, L2 and Lz operators and their commutation relation.

3. The attempt at a solution

For the ψ2p-1 pure state, it is clear that H, L2 and Lz form a CSCO.

For the ψ2px pure state, H and L2 are commuting observables, but not Lz because px=1/21/2(p+1-p-1) and it is not an eigenfunction of Lz. Could yoy give me any additional hint in order to solve it?

For the ψ2s, L2 is equal to zero, so no angular momentum can be measured. Which observable can I use apart form hamiltonian?