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### Finite square well and continuity [duplicate]

In solving finite square well problem, we solve the TISE inside and outside the well, and we match the wave function at the boundary, by the continuity of wave function. Now this bugs me, since the ...
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### Smoothness constraint of wave function

Is there anything in the physics that enforces the wave function to be $C^2$? Are weak solutions to the Schroedinger equation physical? I am reading the beginning chapters of Griffiths and he doesn't ...
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### Rectangular window $\psi$ wave-function and the calculus of $\langle p^2\rangle$ for it

I'm currently considering a rectangular window $\psi$ function: $$\psi(x) = \begin{cases}\left(2a\right)^{-1/2}&\text{for } |x|<a \\ 0&\text{otherwise.} \end{cases}$$ I am interested in ...
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### Does the wavefunction need to be continuous and satisfy other boundary conditions?

So, please don't ignore this question thinking it's a duplicate or something. I have read all the answers on StackExchange and in other articles, but either the math is too confusing, or the answers ...
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### What would be required to get a discontinuous solution of the Schrödinger equation?

I'm thinking about the possibility of a discontinuous solution of the Schrödinger equation and what is needed to get such an object. It should be a condition to the potential, I think. If the ...
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### Discontinuous derivative of wavefunctions in the infinite square well potential problem?

I am intrigued about two points given in an answer to a similar question (https://physics.stackexchange.com/a/38198/262985). On one hand, it is stated that wavefunctions inside the well (excluding ...