Consider a hydrogen atom whose wave function at time t=0 is the following superposition of normalised energy eigenfunctions:
Ψ(r,t=0)=1/3 [2ϕ100(r) -2ϕ321(r) -ϕ430(r) ]
What is the expectation value of the angular momentum squared?
I know that L2 operator is:
-ℏ2 [1/sinθ d/dθ sinθ d/dθ+1/(sin2 θ) d2/dϕ2 ]
although I don't think I need to use it.
I know L2=Lx2+Ly2+Lz2
The Attempt at a Solution
I am confused as to how to go about this. I don't think I need to be calculating an integral, as you would do to find the expectation value of, for example, x2 for a wavefunction. I think I need to calculate the number from squaring the coefficients of each part, and adding, but I'm not sure how to incorporate the L2 bit into this?
I would appreciate any help, I have been puzzling over this for ages now!