# Is it possible to re-write this expression?

#### Xyius

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
$$\psi \frac{\partial \psi^*}{\partial x}$$

in the following form

$$\frac{\partial}{\partial x}(\text{Some function})$$

This is very similar to the following,

$$x \frac{dx}{dt}=\frac{d}{dx}\left( \frac{1}{2}x^2 \right)$$

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

Thanks!

#### wabbit

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 $\psi\frac{\partial\bar\psi }{\partial x}=\frac{1}{2}\frac{\partial}{\partial x}(r^2)-i r^2\frac{\partial \theta}{\partial x}$