How Can You Normalize a Wave Function with Constants C and x0?

[FrankSilliman]

1. $$Find \ C \ in \ terms \ of \ x_0 \ such \ that \ \psi(x,0) \ is \ normalized, \ where \ C \ and \ x_0 \ are \ constants.$$
2. $$\psi(x,0)=Cexp\left (-\frac{\left |x \right |}{x_0} \right )$$
3. $$\\ \psi(x,0)=Cexp\left (-\frac{\left |x \right |}{x_0} \right )\\ \Rightarrow \psi(x,0)=Cexp\left ( -\frac{x}{x_0} \right ) \ for \ x\geq 0 \\ and \ \psi(x,0)=Cexp\left ( \frac{x}{x_0} \right ) \ for \ x<0$$

My thoughts were to split the absolute value up, but I am unsure. Also, I am unsure as to how to choose the bounds for normalizing. Should it just be over (-∞,+∞)?

 

[TSny]

The domain of the function should have been specified. If not, I think you are probably to assume (-∞,∞). It should be clear that the function (and its square) is an even function. So, the integral from -∞ to +∞ can be evaluated by taking twice the integral from 0 to infinity. Don't forget that it's the integral of the square of the function that should equal 1.