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I can come up with normalisable wavefunctions which don't vanish at infinity. However, I cannot come up with a potential so that it satisfies TDSE (the examples I think of are not differentiable at all points). I would appreciate an example.

P.S I'm taking an introductory course in Quantum mechanics and have taken courses on Linear Algebra, Real and Complex analysis and ODEs.

lotsofvodka
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  • [this](https://physics.stackexchange.com/questions/331976/normalizable-wavefunction-that-does-not-vanish-at-infinity?rq=1 question could help – Lorenz Mayer Jan 22 '21 at 09:49
  • Are your non-normalizable wave functuions continuous, differentiable, etc.? Also, keep in mind that the particle number normalization is typical for eigenvalue problems, whereas in scattering problems one more frequently normalizes the particle flux. – Roger V. Jan 22 '21 at 09:56
  • @Vadim Since they should satisfy Schrodinger's equation which has a double spatial derivative, My examples won't qualify because of this requirement. Hence I was looking for an example – lotsofvodka Jan 22 '21 at 16:55

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