Hi, I have a question about the mathematical requirements of a wave function in a potential that is infinite at [tex]x \leq 0[/tex]. (At the other side it goes towards infinity at [tex]x = \infty[/tex].) Now, given a wave function in this potential that is zero for [tex]x = 0[/tex] and [tex]x = \infty[/tex]. Does it matter what that wavefunction is at [tex]x = -\infty[/tex]? I mean, I just figured you would have a wave function there that's zero all the way. Why will a wave function that goes to [tex]-\infty[/tex] at [tex]x = -\infty[/tex] not fit in the (time independent) Schrödinger equation, whereas one that goes to zero at [tex]-\infty[/tex] does? After all when we're normalizing it, we're just integrating from 0 to [tex]\infty[/tex] and doesn't really need to bother with it at negative x values. Or is that just some mathematical requirement that is independent of the physical properties? Can someone enlighten me, please?