In Pauling and Wilson, Introduction to Quantum Mechanics, they offer the following intuitive reason for the discrete spectrum of a potential which is unbounded at $\pm \infty$: This is ...
Usual central potentials produce quantum spectra with energy levels going as $n$, $n^2$, $n^3$ and so on, being $n$ the quantum number of the orbit. In the other extreme we have "dirac-delta" ...
A typical problem where we exploit the uniqueness theorem towards a solution, is finding the potential outside two cylindrical parallel conducting wires (at potentials $V_0$ and $-V_0$) extending to ...
In the paper here(page 7-8) the authors make a claim that the Natanzon potential (an implicit potential) follows an $SO(2,2)$ algebra. This potential defined as : $$ U(z(r)) = ...
I was recently pointed by laboussoleestmonpays to a beautiful paper from some time ago, Aspherical gravitational monopoles. Alain Connes, Thibault Damour and Pierre Fayet. Nucl. Phys. B 490 no. ...
The energy eigenstates of the infinite square well problem look like the Fourier basis of L2 on the interval of the well. So then we should be able to for example make square waves that are an ...
I am reading Shankar's Quantum Mechanics and I am looking at the case where there is one particle inside a box, where the potential is zero inside the wall and abruptly goes to infinity outside the ...
A typical problem in quantum mechanics is to calculate the spectrum that corresponds to a given potential. Is there a one to one correspondence between the potential and its spectrum? If the ...