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## Main Question or Discussion Point

I've heard some people say that the wave function and its first derivative must be continuous because the probability to find the particle in the neighborhood of a point must be well defined; other people say that it's because it's the only way for the wave function to be physically significant. There is even another hypothesis, which states it's a consequence of the eigenvalue equation

H[tex]\Psi[/tex]=E[tex]\Psi[/tex]

Which idea is the right one?

H[tex]\Psi[/tex]=E[tex]\Psi[/tex]

Which idea is the right one?