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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?
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>>7796624
the truth is you don't need a C2 function.
You just need a function in a sobolev space.
I never thought about this before, but now I see that most physics profs don't give two fucks.
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>>7796696
Physics are almost as bad as engineers
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>>7796720
Too bad I'm an engineer then.
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>>7796624
e^ix and delta functions are also not, but they are momentum and position eigenfunctions used to construct tons of solutions.
>But doesn't the SE require that psi be a C^2 function?
The Schrodinger equation is essentially derived from the single assumption of unitary time evolution. In other words, the total probability is conserved in over time, which specifically means in this context that nothing can be destroyed.
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>>7796720
Please.
Engineers just use math; Physicists gang rape and sodomize her.
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