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## Homework Statement

Following gaussian wave packet: ## \psi (x)= \frac{1}{\sqrt{\sqrt{\pi a^2}}} e^{-\frac{x^2}{2a^2}}##

Prove that this function is normalized.

## Homework Equations

## \int_{- \infty}^{\infty} |\psi (x)|^2 dx = 1##

## The Attempt at a Solution

Is ## \frac{1}{\sqrt{\sqrt{\pi a^2}}} \int_{- \infty}^{\infty} e^{-\frac{x^2}{a^2}} dx## equal to 1?

I have a solution given, but I don't really get how they even got that solution:

## \frac{1}{\sqrt{\pi a^2}} \sqrt{\pi a^2}## = 1

But that solution totally ignores the double root in the first term, and I'm mond boggled how they managed to integrate the exponent to ending up as ##\sqrt{\pi a^2}##? Actually I don't manage to clearly and unambiuously integrate that exponent myself.