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Eigenfunctions of angular momentum operators in momentum representation

Just a point to make. In consdering the transformation one has to have the time reversal go as $$T|rlm\rangle ~=~ (-1)^{l+m}|rl-m\rangle$$ irrespective of the representation which leads to $$\langle \...
SAKhan's user avatar
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2 votes

Analytic approximation of bound state energies for finite square well

I will set $a=2$ with no loss of generality. Your equations are: $$ \sqrt{K^2-k^2} = k\tan k \quad \sqrt{K^2-k^2} = -k\cot k $$ and you want the roots in the limit $K\to\infty$ i.e. the infinite well ...
LPZ's user avatar
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1 vote

Can the non-degenerate perturbation theory formula for higher-order energy corrections be used in case of degenerate perturbation theory?

OP's linked reference (Ref. 1) shows in eq. (1.2.5) that OP's eq. (1.1.26) with $s=1$ may be violated for degenerate (time-independent) perturbation theory. For $s=1$ one needs to impose an additional ...
Qmechanic's user avatar
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4 votes

The problem with commutation relation

Classic error. The inequality holds only if the states are normalized, and the eigenstates of $Q$ are not - at least not normalized in the usual sense as they are outside the usual Hilbert space. ...
ZeroTheHero's user avatar
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