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perplexabot
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Homework Statement
The allowed magnitudes of angular momentum are L = √(l(l+1)) * hbar. Use the binomial expansion to prove that when l is large, L ≈ (l + .5) * hbar.
Homework Equations
Binomial expansion formula: (1 + z)^n = 1 + nz + [n*(n-1)*z^2] / 2 + ...
The Attempt at a Solution
Ok. First I did:
L = √(l(l+1)) * hbar = [hbar * √l] * [1 + l]^.5
Then doing Bin. expan. apprx. for [1 + l]^.5,
I get a final answe, L ≈ hbar * √l * (1 + l/2)
Which is wrong. When compared to L ≈ (l + .5) * hbar, I can tell that I have an extra factor of √l, I think it has something to do with l being very large. Can someone please help me out? Thanks
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