Trouble with the semi-infinite well (a tale of quantum confusion)

Hi all. I'm having some troubles with my quantum physics studies. I
understand an have solved the Schroedinger equation for the case of
the infinite and finite square wells in one dimension, however the
combination of the two is giving me a real headache.

The basic problem is this V=infinity if x<0, V=0 if 0<x<L, and V=V_0
if x>L set up and solve the Schroedinger wave equation analytically.

Here's what I've done in as few words as possible, I'm going to use
Z_n to stand for Psi:

Z_1=0 , x<0
Z_2=A*sin(k_1*x)+B*cos(k_1*x) , 0<x<L
Z_3=C*exp(k_2*x)+D*exp(-k_2*x) , x>L

Applying the trivial boundary conditions that Z_2=0 @ x=0 and Z_3 goes
to 0 as x goes to infinity I find that B=C=0. So I have:


Z_1=0 , x<0
Z_2=A*sin(k_1*x) , 0<x<L
Z_3=D*exp(-k_2*x) , x>L

I then equate Z_2 and Z_3 @ x=L and do the same with their first x
derivatives to obtain:

A*sin(k_1*x)=D*exp(-k_2*x) and k_1*A*sin(k_1*x)=-k_2*D*exp(-
k_2*x)

Then I apply the normalization requirement and find that:

A^2 * [ L/2 - sin(2 * k_1 * L) / (4 * k_1) ] - D^2 / (2 * k_2) *
exp( - 2 * k_2 * L ) = 1

It is at this point where I become kind of lost. I just cannot seem
to find the constants A and D. This leads me to believe that I've
done something in correct in my derivation up to that point, that or I
am missing something.

Now I am certainly not looking for someone to do this for me but if I
could get a little direction it would really kick ass.

Thanks,
Patrick
.

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