(adsbygoogle = window.adsbygoogle || []).push({}); 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 [2ϕ_{100}(r) -2ϕ_{321}(r) -ϕ_{430}(r) ]

What is the expectation value of the angular momentum squared?

2. Relevant 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}

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, 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!

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# Homework Help: Finding the expectation value of the angular momentum squared for a wave function

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