New answers tagged eigenvalue
0
votes
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
$$\langle \...
2
votes
Analytic approximation of bound state energies for finite square well
I will set $a=2$ with no loss of generality. Your equations are:
$$
\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 ...
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 ...
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. ...
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