# Wave function evaluation

1. Mar 29, 2012

### facenian

1. The problem statement, all variables and given/known data
This problem is in Schaum's outline of quantum physics. We need to evaluate $$|\psi(x)|^2$$ for the wave function $$\psi(x)=\int_{-\infty}^{\infty}e^{-|k|/k_0}e^{ikx} dk$$

2. Relevant equations
$$|\psi(x)|^2=\psi(x)\psi(x)^*$$

3. The attempt at a solution
I tried to evaluate the integral $$\int_{-\infty}^{\infty}dk\int_{-\infty}^{\infty}dk'e^{-(|k|+|k'|)/k_0}e^{i(k-k')x}$$

Last edited: Mar 29, 2012
2. Mar 29, 2012

### vela

Staff Emeritus
The integral should be with respect to k, not x. You can evaluate it. Give it a shot.

3. Mar 29, 2012

### facenian

yes it should be with respect to k not x. Can you give me same hint. Is it correct trying to evaluate it as I wrote in my attempt at a soluciont? or should I evaluate $$\psi(x)$$directly? or me be use the residue technique?

Last edited: Mar 29, 2012
4. Mar 29, 2012

### vela

Staff Emeritus
I'd just integrate it directly. There's no need to do anything fancy here.