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**[SOLVED] Probability Current for Free Particle Wave Function**

## Homework Statement

Find the probability current, J for the free particle wave function. Which direction does the probability current flow?

## Homework Equations

[tex]J(x,t) = \frac{ih}{4\pi m}\left(\Psi \frac{\partial \Psi^{*}}{\partial x} - \Psi^{*} \frac{\partial \Psi}{\partial x}\right)[/tex]

[tex]\Psi_{k}\left(x, t\right) = Ae^{i\left(kx - \frac{hk^{2}}{4\pi m}t}\right)[/tex]

## The Attempt at a Solution

I won't take the time to put my math into Latex, but I come up with

[tex]J(x,t) = \frac{A^{2}hk}{2\pi m}[/tex]

Is this correct or did I do the complex conjugate wrong?

How would I find the probability current flow direction?

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