# Finite Square Well, Ψ[SUB]III[/SUB] const related too Ψ[SUB]II[/SUB]?

The Floating Brain
Homework Statement:
There are two ledges with of U potential energy, and a cavern in between them of 0 potential energy. Such that

U(x) = { x <= 0, U, x > 0, x >= L, U }

Find the probability distribution for all 3 regions
Relevant Equations:
(ħ[SUP]2[/SUP]/2m)((d[SUP]2[/SUP]Ψ)/(dx[SUP]2[/SUP]) + U(x)v = EΨ

∫ Ψ * Ψ dx = 1
I'm following Griffith's Modern Physics 2nd edition chapter 5.

I got to the part where we make ΨI(0) = ΨII(0) I get that

αCeα(0) = QAsin(Q(0)) - QBsin(Q(0)) => C = QA/α

But when I try to graph it, the region I distribution doesn't seem to equal the region II distribution at 0.

The book goes on on to insert C into an equation to solve for G (-αGe-α(L) for the other side of the well), but I don't understand why it does this.

-αGe-α(L) = (αC/Qs)sin(Q(L)) + C/cos(Q(L))

Why does what happens on one side affect what happens on the other?

• Delta2

Staff Emeritus
Homework Helper
Homework Statement:: There are two ledges with of U potential energy, and a cavern in between them of 0 potential energy. Such that

U(x) = { x <= 0, U, x > 0, x >= L, U }

Find the probability distribution for all 3 regions
Relevant Equations::2/2m)((d2Ψ)/(dx2) + U(x)v = EΨ

∫ Ψ * Ψ dx = 1

I'm following Griffith's Modern Physics 2nd edition chapter 5.

I got to the part where we make ΨI(0) = ΨII(0) I get that

αCeα(0) = QAsin(Q(0)) - QBsin(Q(0)) => C = QA/α

But when I try to graph it, the region I distribution doesn't seem to equal the region II distribution at 0.
Your graph doesn't correspond to your work above. Back up a bit and tell us what you're using for ##\psi_I## and ##\psi_{II}##. And how did you get rid of ##B## to solve for ##C## from one equation?