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2016-01-20 00:41:32 Post No. 7796624
Post No. 7796624
Griffiths says that when the potential becomes infinite, the boundary condition there that requires the wave function to be first-order continuously differentiable no longer applies (e.g. in the figure I posted, it's clearly no longer differentiable at the boundaries). But doesn't the SE require that psi be a C^2 function? Why are we allowed to just throw away this property?
My only guess is that, since infinite potentials aren't realistic, and used just to demonstrate some basic techniques, we do some massive handwaving. But what about a rigorous treatment (e.g. dirac delta potential)? Is there a way to make a properly C^2 wave function in an infinite potential well?