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## Homework Statement

A quantum mechanical wavefunction for a particle of mass m moving in one dimension where α and A are constants.

Normalize the function - that is find a value of A for which [tex]\int^{\infty}_{-\infty}|ψ|^2dx=1[/tex]

## Homework Equations

[tex]ψ(x,t)= |Ae^{-α(x^2 + it\hbar/m)}|^2[/tex]

A useful integral: [tex]\int^{\infty}_{-\infty}e^{-z^2}dz = √\pi[/tex]

## The Attempt at a Solution

[tex]ψ(x,t)= |Ae^{-α(x^2 + it\hbar/m)}|^2[/tex]

[tex]1= \int^{\infty}_{-\infty}|Ae^{-α(x^2 + it\hbar/m)}|^2 [/tex]

[tex]1= |A|^2\int^{\infty}_{-\infty}(e^{-α(x^2 + it\hbar/m)})(e^{α(x^2 + it\hbar/m)})[/tex]

I'm pretty sure the last line is incorrect. My reasoning was that since i is a complex number, for all complex numbers |z|^2≠|z^2z|. Before this, I tried changing the variable by letting [tex]z=√(2α(x^2 + it\hbar/m))[/tex]