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#### skatenerd

##### Active member

- Oct 3, 2012

- 114

So I have

$$\psi(x)=Ne^{-\frac{|x-x_o|}{2a}}$$

And the formula for normalizing this to find \(N\) would be

$$\int_{-\infty}^{\infty}\bar{\psi(x)}\psi(x){dx}=1$$

Plugging in \(\psi(x)\) gives

$$1=\int_{-\infty}^{\infty}N^{2}e^{-\frac{|x-x_o|}{a}}dx$$

At first I was thinking I could just take the derivative of the exponent and divide by that to solve the integral but I realized that wouldn't work out right, and this integral behaves somewhat like a gaussian integral like when you need to integrate \(e^{-x^2}\).

I know the process of how to integrate \(e^{-x^2}\) from negative infinity to infinity (defining the integral as I and then squaring it, changing to polar coordinates, u-subbing and then taking the root of that solution to get \(\sqrt{\pi}\)) but when I tried to do that with \(\frac{|x-x_o|}{a}\) instead of \(x^2\) I end up with a weird expression in the exponent that I don't know what to do with. I was hoping changing to polar coordinates would work but I don't see how to do that with this.

Any guidance would be really appreciated! Thanks