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ever.monk

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Often for certain situations there are multiple (atleast in mathematic form) solutions to the schrödinger Eq. Are these all the same? eg.

Famous infinite potential well. 2 solutions are Psi=Asin(kx) but also powers of e are possible. When entirely normalized, etc, are they essentially the same probability distribution?

With tunneling, the wave function is shown to have a value in the V>E area. But this would mean that there is a possibility of finding it here, which is nonsense. If this probability would be disregarded, wouldn't this disturb the normalizing of the wavefunction? (the V>E would still be part of the normalization :S) This would the same with a finite potential well, as there are results for the wavefunction in V>E areas. How does normalizing work in these situations?

And one last question. Are wavefunctions are purely attained through solving things like the schrödinger equations, or can they also attained through other means?

It would help my understanding a lot of you help my out with this curiosities.