What is the physical basis for the requirement that the wave function has finite and continuous first order derivative?

tom.stoer
b/c only then it carries finite momentum and energy in a finite interval

$$\int_{x-\epsilon}^{x+\epsilon}dy\,\psi^\ast\,(i\partial_y)\,\psi$$

$$\int_{x-\epsilon}^{x+\epsilon}dy\,\psi^\ast\,(-\partial^2_y)\,\psi$$

Thank you.That really helped me a lot.

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