Is it possible to re-write this expression?

  • Thread starter Xyius
  • Start date
507
4
Hello everyone,

I am trying to develop a model for my PhD research, I don't want to get into specifics too much, but I have encountered the following problem.

I need to write
[tex]\psi \frac{\partial \psi^*}{\partial x}[/tex]

in the following form

[tex]\frac{\partial}{\partial x}(\text{Some function})[/tex]

This is very similar to the following,

[tex]x \frac{dx}{dt}=\frac{d}{dx}\left( \frac{1}{2}x^2 \right)[/tex]

However the fact that ##\psi## is a complex number is making this difficult for me. Does anyone have any ideas??

Thanks!
 

wabbit

Gold Member
1,284
207
This doesn't seem likely - ## \frac{\partial }{\partial x}(\psi\bar\psi)=\psi\frac{\partial\bar\psi }{\partial x}+\frac{\partial\psi }{\partial x}\bar\psi ## is the analogue to the identity you write but it only gives you a similar result for the real part. Similarly if you write ## \psi=r e^{i\theta} ## you get ## \psi\frac{\partial\bar\psi }{\partial x}=\frac{1}{2}\frac{\partial}{\partial x}(r^2)-i r^2\frac{\partial \theta}{\partial x} ##
 

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