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IHateMayonnaise

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**[SOLVED] Particle in a box**

## Homework Statement

A particle is described by the wave function [tex]\Psi(x)=Ae^{(-bx^2)}[/tex]. Calculate the normalization factor A.

## Homework Equations

&## The Attempt at a Solution

So, to normalize [tex]\psi(x)[/tex], we integrate the probability ([tex]\Psi(x)^2[/tex]) over the entire area (this is in an infinite potential well, so let's say the particle is between x=0 and x=L) and set this equal to 1. Doing this, we have:

[tex]A^2\int_0^L{e^{-2bx^2}}dx=1}[/tex]

I feel pretty comfortable with calculus but I cannot figure out how to evaluate this integral. I was able to find this in an integral table, but it wasn't much help:

[tex]\int e^{ax^2} dx = -\frac{i\sqrt{\pi}}{2\sqrt{a}}\text{erf}\left(ix\sqrt{a}\right)[/tex]

I do not recall learning anything about the error function (erf), and google wasn't much help. How can I evaluate this integral? Should I expand it in series? Any help would be appreciated. Thanks

IHateMayonnaise

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