# Potential well solutions question

1. Mar 18, 2012

### physicsjock

Hey,

I've been trying to work out how, for a finite well of high Vo and width L, the interior solution has the form L Sin(kx + d),

I see that if d=0 then the solution resembles an infinite well, so that implies d depends inversely on the wells potential. But I can't work out what d comes from, and why the constant at the front is the length of the well (why is the amplitude of the wave the length of the well)

d is just the phase of the wave, so does it represent an adjustment to assure all the continuity requirements are satisfied?

Ive also been trying to work out what the k is, when I go through the process of finding the wave function inside I end up with (s/k)Asinkx + Acoskx after applying the boundary conditions.

where k2=2mE/$\hbar^{2}$

and s2=2m(Vo-E)/$\hbar^{2}$

i've been trying to work this out because ive also read that the below equation should also satisfy the internal solutions

ka = n$\pi - 2Sin^{-1}(\frac{k\hbar}{\sqrt{2mV_{o}}})$

this makes it seem like d resembles the inverse sin term, which makes sense because if Vo ->infinity you would get the solution to an infinite potential well

Anyone have any ideas?