1. The problem statement, all variables and given/known data 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? 2. Relevant equations 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 3. 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!