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mar0
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I take Schrödinger Equation and look for spherically symmetric stationary state wave function. I make substitution [tex]\sigma (r) = r X(x)[/tex] get simpler form. This equation is defined for [tex] r \geq 0 [/tex] , Boundary Conditions is that wavefunction is finite at all points. Now It is possible to relate nicely with one dimensional case by extending potential to be even and define [tex] r [/tex] on the whole real line.
My question is: Probably I am lacking mathematical insight, but why such substitution relates so perfectly well? Then further boundary condition is that [tex]\sigma (r)[/tex] is normalizable, or actually what we really need is square integrable for [tex] r \geq 0 [/tex]. What are further constraints for this "wave function"? It must be either odd or even. My textbook says it must be odd, so why is that?
Original wave function will be finite at origin provided [tex]\sigma (r)[/tex] is zero there.
Many thanks.
///Never mind (probably this was supposed to be in homework section anyway)
My question is: Probably I am lacking mathematical insight, but why such substitution relates so perfectly well? Then further boundary condition is that [tex]\sigma (r)[/tex] is normalizable, or actually what we really need is square integrable for [tex] r \geq 0 [/tex]. What are further constraints for this "wave function"? It must be either odd or even. My textbook says it must be odd, so why is that?
Original wave function will be finite at origin provided [tex]\sigma (r)[/tex] is zero there.
Many thanks.
///Never mind (probably this was supposed to be in homework section anyway)
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