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### Bound states of the $V(x)=\pm \delta'^{(n)}(x)$ potential?

The $\delta(x)$ Dirac delta is not the only "point-supported" potential that we can integrate; in principle all their derivatives $\delta', \delta'', ...$ exist also, do they? If yes, can we look for ...
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### Bound states in 1D & 2D [duplicate]

Why does Mother Nature allow bound states in arbitrarily weak attractive potential in 2D but not in 3D? See, for example, this article, arXiv:math-ph/0208011.
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### How to predict bound states in a 1D triangular well?

Assume we have a (single) particle in a potential well of the following shape: For $x \leq 0$, $V = \infty$ (Region I) For $x \geq L$, $V = 0$ (Region III) For the interval $x > 0$ to $x < L$,...
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### How can theories about 1D or 2D systems be generalized for 3D systems?

I was watching a lecture video from MITx $^\dagger$ by professor Barton Zwiebach. He proved a pretty cool theorem "every attractive 1-dimensional potential has a bound state"; however, that only holds ...
The following is the problem that I'm struggling with from the book of Gasiorowicz: If we have an electron in a potential well of width $a$ and depth $V_0$, then the kinetic energy is, by the ...