 #1
The Floating Brain
 11
 1
 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 Ψ_{I}(0) = Ψ_{II}(0) I get that
αCe^{α(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?
I got to the part where we make Ψ_{I}(0) = Ψ_{II}(0) I get that
αCe^{α(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?