Normalization of a wave function with cosine

1. Oct 21, 2007

wakko101

I need to normalize the following wave function:

psi= Cexp(-abs(x))exp(-iwt)cos(pix)

I know that when squaring it, the time dependent part drops out, which is good, but what I seem to be left with is

Psi^2=C^2exp(-2abs(x))cos^2(pix)

Which seems like a fairly complicated integral to compute. I'm thinking that there is something that I'm missing about this particular wave function that will make it easier to integrate?

Any help?

Cheers,
wakko =)

2. Oct 21, 2007

Dick

Split it into x>0 and x<0 parts. For the positive part drop the abs. The negative part is the same since the integrand is even.

3. Oct 21, 2007

wakko101

That's not really the problem I'm having...I understand that I can double the integral over 0 to infinity, I'm just wondering if there is a simpler way to to figure out the integral itself.

Thanks anyway.

4. Oct 21, 2007

Dick

cos(pi*x)=(exp(i*pi*x)+exp(-i*pi*x))/2. If you do it that way you can turn the whole thing into one big exponential. Otherwise you can integrate by parts. It IS a somewhat complicated integral to compute. But not the worst.

5. Oct 21, 2007

wakko101

but if I do the conversion, I end up with an integrand that has i still in it, don't I? that doesn't seem right to me....

6. Oct 22, 2007

Dick

It will seem right when all of the i's cancel in the end.

7. Oct 22, 2007

clem

It's a bit easier to use cos x=Re[exp(ix)]