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## Homework Statement

Given a wave function psi, [itex]\psi (x) = A \sqrt{|x|} e^{- \beta x^2} [/itex] where [itex]\beta[/itex] is a constant (take the positive square root) . Normalise the wave function and hence find A.

## Homework Equations

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## The Attempt at a Solution

This is my first attempt at a problem like this, and I have missed around a 1/3 of the lectures on this this semester due to being ill.

Where it says that beta is a constant, I assumed that mean real, but even if its imaginary I still cant do it.

First if it is real then

[tex]

\int_{-\infty}^{\infty} |\psi|^2 \> dx= 1 \\

\int_{-\infty}^{\infty} |A|^2 |x| e^{- 2 \beta x^2} \> dx = 1 \\

|A|^2 \int_{-\infty}^{\infty} |x| e^{- 2 \beta x^2} \> dx = 1

[/tex]

But in a formula book we were given it says that that integral equals 0 , so I tried if it was complex then

[tex]

\int_{-\infty}^{\infty} |\psi|^2 \> dx= 1 \\

\int_{-\infty}^{\infty} |A|^2 |x| e^{- \beta x^2} e^{ \beta x^2} \> dx = 1 \\

|A|^2 \int_{-\infty}^{\infty} |x| \> dx = 1

[/tex]

Then how do I proceed from there, as surely [itex][\frac{1}{2}|x|^2]_{-\infty}^{\infty}[/itex] is just infinite?

I dont even know if if my method for the two cases is even correct. Please any help/advice is much appreciated, I have been looking at this problem for the past 3 hours, looking at the lecture notes, and online and I am really lost!

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