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Is it possible to re-write this expression?

  1. May 14, 2015 #1
    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??

  2. jcsd
  3. May 14, 2015 #2


    User Avatar
    Gold Member

    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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