Can the wave function be evaluated using the integral method?

[facenian]

Homework Statement

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

Homework Equations

$$|\psi(x)|^2=\psi(x)\psi(x)^*$$

The Attempt at a Solution

I tried to evaluate the integral $$\int_{-\infty}^{\infty}dk\int_{-\infty}^{\infty}dk'e^{-(|k|+|k'|)/k_0}e^{i(k-k')x}$$

 

[vela]

Homework Statement

This problem is in Schaum's outline of quantum physics. We need to evaluate $$|\psi(x)|^2$$ for the wave function $$\psi(x)=\int_{-\infty}^{\infty}e^{-|k|/k_0}e^{ikx} dx$$

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

Homework Equations

$$|\psi(x)|^2=\psi(x)\psi(x)^*$$

The Attempt at a Solution

I tried to evaluate the integral $$\int_{-\infty}^{\infty}dk\int_{-\infty}^{\infty}dk'e^{-(|k|+|k'|)/k_0}e^{i(k-k')x}$$

 

[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?

 

[vela]

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