## Particle in a box... wave function problem

I have a wave function problem that I need to figure out... I have a really borderline grade, so it could mean the difference between an 'A' and a 'B' in my graduate Modern Physics class.

Basically, I have to figure out the wave function and the transmission and reflection coefficients. My professor did a really crappy job of explaining this stuff in class, so I'm totally lost.

Here's the question:
Consider a potential with the following shape:

What are the wave functions for all regions of the problem is a particle beam approaches the barrier from negative infinity with an energy E? Find the reflection and transmission coefficients.
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 Start by breaking down the potential into 4 parts, and solving the Schrodinger equation for each.
 That's what I thought I'm supposed to do, but I'm not sure if I'm doing it right. Does that mean that I need to plug it into psi(x) = [(2/L)^(1/2)] [sin(n*pi*x/L)] ? My professor didn't do a very good job of explaining Schrodinger's equation, so I don't have a very thorough understanding of it. Also, does "reflection" and "transmission" coefficients just mean that I need to plug it into these equations? http://upload.wikimedia.org/math/0/f...1235a4ffaf.png http://upload.wikimedia.org/math/0/f...1235a4ffaf.png

## Particle in a box... wave function problem

The Schrodinger equation, among many things, gives you a differential equation for Psi, of which, based on your potential energy, you can solve for Psi. I'd look it up on Wikipedia (you want the time independent form) so you can get practice solving it (it's actually not that bad for the potentials given). And for the reflection and transmission coefficients, those will not be the answer. Those are for a different potential (a single finite barrier I think, but that's just an inspective guess.)
 Recognitions: Science Advisor You have four regions: x<-a, -ab, which I will call R1, R2, R3, and R4. In each region, you solve the time-independent Schr eq. For a consant potential, the most general solution is of the form A e^(ikx) + B e^(-ikx), except possibly in R3; the solution is of this form if E>V0, but takes the form A e^(kx) + B e^(-kx) if EV0 case; if you solve this one, you can get the solution to the E
 Thanks a lot! So basically, the first step is to figure out each k and solve the equation for psi? I guess that k2 and k3 are the same as k1 and k4, except that I replace "E" with "V-E", right?

Recognitions:
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