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## Homework Statement

Consider the wave function

[tex]\Psi(x, t) = Ae^{-\lambda|x|}e^{-i\omega t}[/tex]

where A, [tex]\lambda[/tex] and [tex]\omega[/tex] are positive real constants.

Normalize [tex]\Psi[/tex]

## Homework Equations

[tex]\int |\Psi(x, t)|^{2} dx = 1[/tex]

[tex]|\Psi(x, t)|^{2} = \Psi^{*}\Psi[/tex]

## The Attempt at a Solution

I have a model solution - with a step missing, I think my error is in complex conjugate math...

1, Finding [tex]|\Psi(x, t)|^{2}[/tex]

[tex]\Psi^{*}\Psi = (Ae^{-\lambda|x|}e^{i\omega t}) (Ae^{-\lambda|x|}e^{-i\omega t})[/tex]

[tex] = A^{2}e^{-2\lambda|x|}e^{i\omega t}e^{-i\omega t}[/tex]

[tex] = A^{2}e^{-2\lambda|x|}e^{0} = A^{2}e^{-2\lambda|x|}[/tex]

I think this is where my problem is, I am told that

[tex]|\Psi(x, t)|^{2} = 2|A|^{2}e^{-2\lambda|x|}[/tex]

So I am missing a factor of 2?

Is there a complex conjugate rule somewhere I am missing?