- #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

αCe

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

-αGe

I got to the part where we make Ψ

_{I}(0) = Ψ_{II}(0) I get thatαCe

^{α(0)}= QAsin(Q(0)) - QBsin(Q(0)) => C = QA/αBut 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?