# Quantum Mechanics Problem: Quick help kindly requested

1. Nov 28, 2007

### bktennis2006

1. The problem statement, all variables and given/known data

1. Suppose we have a potential V(x) which is zero everywhere except 0<x<a, where it is equal to –Vo, where Vo is positive (and thus –Vo is negative). For the case where E > 0, it asks

a. to give the form of the wavefunctions in all three regions, defining k1, k2 and k3 properly.
b. for scattering off the potential by particles coming in from the left, determine what wavefunction amplitudes can be set to zero.
c. derive appropriate boundary conditions relating wave function amplitudes at the boundaries between regions.

2. It then asks to answer the same question using the case where E < 0, and also for b. it asks to determine which wavefunctions should be set to zero for bound states.

3. Solve explicitly for the transmission coefficient in Problem 1, and in what cases is the coefficient exactly 1?

2. Relevant equations

The time-independent Shrodinger equation, of course.

3. The attempt at a solution

Unfortunately, I was only able to find the wavefunctions in #1, and I don't even know if they're right. I did it by solving for $$\psi$$ using the Shrodinger equation, but does it also want $$\Psi$$? The second part of both #1 and #2 confuse me, as I don't even know what they're asking for.

Any help would be greatly appreciated, but unfortunately the problems are due today, so a quick response would be greatly appreciated...thanks!

2. Nov 28, 2007

### robphy

So, what did you get for #1?

Once you have that... what does it mean to have "particles coming in from the left"?