- #1

Ruddiger27

- 14

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There's a particle of mass moving in a potential well where

V(x) = infinity at x<0

V(X)=0, 0<x<a

V(x)= Vo, x>a

Vo>0

E<Vo

I'm assuming that the wavefunction at x<0 is 0, since there's an infinite potential there. The energy inside the potential well is just the kinetic energy, =(Hk)^2/2m, where H=h/2pi, so the wavefunction should be of the form

psi= Aexp(-ikx )

Now outside the well, at x>a, the energy should be E= Vo-Ek because the particle is bound in the well. We then get psi=Bexp(-Tx), where T is k with (Vo-E) instead of E.

Am I wrong in assuming this? When I try to find the radius using

X^2 + y^2 = R^2, where x=k=a*sqrt(2mE)/H and y=ai*(sqrt(2m(Vo-E))/H

I get out a negative radius.

Please help me see what I've done wrong, I'm sure I've got the energy value on the finite potential side wrong, but I can't see how.