What Are the Solutions to the 1D Infinite Square Well from -a/2 to +a/2?

[siifuthun]

I think I'm on the right track for this problem, but I'm not entirely sure.

Find the solutions to the one-dimensional infinite square well when the potential extends from -a/2 to +a/2 instead of 0 to +a. Is the potential invariant with respect to parity? Are the wave functions? Discuss the assignment off odd and even parity to the solution

So the wave functions should look the same as if it was an infinite square well going from 0 to +a, except it's going from -a/2 to a/2, so the parity should be exactly the same, right? V(x) = infinity at x< -a/2 and when x> a/2.

So I tried solving for the Schrödinger equation using:

http://img145.imageshack.us/img145/4013/03bp1.jpg

And we know that at -a/2 and a/2, the wavefunction must be equal to 0. We also know that for energy level E_1, where n=2, there's a node right at x=0, so the wavefunction must also equal 0 at x = 0 for that case. So:

http://img174.imageshack.us/img174/4408/04ya7.jpg

So we know from above that B=0, plugging that into equation we get:

http://img98.imageshack.us/img98/5520/05ep7.jpg

Now here's my problem, when I try to solve this, I get:

http://img170.imageshack.us/img170/5769/06vs2.jpg

Which is a problem, since it means A=0. Am I wrong in my assumption that the wavefunction for E_1 state is 0 at x=0?

 

[feb2_sg]

There might be a problem with the last statement of E_1 state is 0 at x=0
.
Why do you think that is so?

 

[feb2_sg]

Problem with integration

I finally managed to find out what the heck it was. There is a problem with the integration of the function. Try using http://integrals.wolfram.com/index.jsp. Very useful mathematical program.