Normalization of a wave function with cosine

[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 =)

 

[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.

 

[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.

 

[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.

 

[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...

 

[Dick]

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

 

[Meir Achuz]

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