# Determining Normalization Constant

1. Aug 29, 2011

### atomicpedals

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

Determine the normalization constant c in the wave function given by
$\psi$(x) = c cos(kx) exp[(-1/2)(x/L)2 ]

2. Relevant equations

1=$\int$ |$\psi$(x)|2 dx

limits of integration being -inf to inf.

3. The attempt at a solution

I'm very much sure that my math is wrong, I'm very rusty with improper integrals.

1= $\int$ |c cos(kx) exp[(-1/2)(x/L)2|2 dx

= $\int$ |c2 cos2(kx) exp[-(x2/L2)| dx

it's at this point I start getting into trouble

= c2 $\int$ |cos2(kx) exp[-(x2/L2)| dx

= c2 $\int$ cos2(kx)dx $\int$ exp[-(x2/L2)dx

= c2 (lim((2kx+sin(2kx))/4k)) ($\pi$)1/2/(1/L2)1/2

I think I'm pretty solidly wrong by this point... where did I go wrong?

2. Aug 29, 2011

### LaissezDairy

You can't break up an integral like that. Think about it.

$\int x^2 dx = \int x * x dx = \int x dx \int x dx = x^4/4$ ??

Also this identity might make it less painful for you:

$cos(kx) = \frac{e^{ikx} + e^{-ikx}}{2}$ (Euler's formula)

3. Aug 29, 2011

### atomicpedals

Ah, right... well at least I made it three steps in before totally going off the deep end. Still working on it though.

4. Aug 29, 2011

### atomicpedals

So my sticking point mathematically really seems to be the

e(-1/2)(x/L)2

This almost certainly simplifies down to something reasonably basic after being squared and/or integrated shouldn't it?

Last edited: Aug 29, 2011
5. Aug 30, 2011

### LaissezDairy

do you know what a gaussian integral is?

6. Aug 30, 2011

### atomicpedals

Yep, Arfken is a life-saver!