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## Homework Statement

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 [2ϕ

_{100}(r) -2ϕ

_{321}(r) -ϕ

_{430}(r) ]

What is the expectation value of the angular momentum squared?

## Homework Equations

I know that L

^{2}operator is:

-ℏ

^{2}[1/sinθ d/dθ sinθ d/dθ+1/(sin

^{2}θ) d

^{2}/dϕ

^{2 }]

although I don't think I need to use it.

I know L

^{2}=L

_{x}

^{2}+L

_{y}

^{2}+L

_{z}

^{2}

## 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, x

^{2}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 L

^{2}bit into this?

I would appreciate any help, I have been puzzling over this for ages now!