(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I have a wave function,

[tex]\psi(x)=Ae^{ik_{0}x-ax^{2}}[/tex]

All I am required to do is calc. the prob. current. This I have done using the usual

[tex]j = \frac{\hbar}{m}.|A|^{2}.\frac{\partial \varphi}{\partial z}[/tex]

where [tex]\varphi}[/tex] is the imaginary component of the exponent of e.

It comes (of course) to [tex]j = \frac{\hbar}{m}.|A|^{2}.k_{0}[/tex].

But, doing it the long way (I just thought I would), with

[tex]j = \frac{\hbar}{2mi}.(\psi*\frac{\partial\psi}{\partial x}-\psi\frac{\partial\psi*}{\partial x})[/tex]

I end up with the same result, but [tex]e^{-2ax^{2}}[/tex] attached. Since taking [tex]\psi*[/tex] only changes the sign of the imaginary component, this seems inevitable... anyone know what I'm doing wrong?

Cheers :-)

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# Homework Help: Probability current

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