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## Homework Statement

Calculate the probability current density vector [itex]\vec{j}[/itex]for the wave function [itex]\psi = Ae^{-(wt-kx)}[/itex].

## Homework Equations

From my very poor and beginner's understanding of probability density current it is :

[itex]\frac{d(\psi \psi^{*})}{dt}=\frac{i\hbar}{2m}[\frac{d\psi}{dx}\psi^{*}-\frac{d\psi^{*}}{dx}\psi][/itex]

## The Attempt at a Solution

By applying the RHS of the above equation :

[itex]\frac{i\hbar}{2m}[-A^{2}ikxe^{-i(ωt-kx)}e^{i(ωt-kx)}-A^{2}ikxe^{i(ωt-kx)}e^{-i(ωt-kx)}][/itex]

This gives :

[itex]\frac{-2iA^{2}ik\hbar}{2m}=\frac{k \hbar A^{2}}{m}[/itex]

This is not the correct answer. :( What have I done wrong ?

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