Is it possible to re-write this expression?

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In summary, the conversation discusses the difficulty of writing a specific mathematical expression involving a complex number in a desired form. The participants suggest different approaches, but it is noted that the complex nature of the number makes it challenging.
  • #1
Xyius
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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!
 
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  • #2
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} ##
 

FAQ: Is it possible to re-write this expression?

Can an expression be rewritten without changing its meaning?

Yes, it is possible to re-write an expression without changing its meaning. This is often referred to as simplifying or rephrasing the expression. The new expression may use different words or symbols, but it should still convey the same idea or concept.

What are some reasons for re-writing an expression?

There are several reasons why one might want to re-write an expression. One common reason is to make the expression easier to understand or more concise. Another reason could be to use a different notation or format that is more suitable for a specific context or audience.

Is it always necessary to re-write an expression?

No, it is not always necessary to re-write an expression. If the original expression is clear and easily understood, there may be no need to change it. However, re-writing can be beneficial to improve clarity or to conform to a specific format or style.

Are there any rules or guidelines for re-writing an expression?

There are no strict rules for re-writing an expression, but there are some general guidelines that can be followed. These include maintaining the same meaning, using appropriate notation and symbols, and ensuring the expression is clear and concise. It is also important to consider the context in which the expression will be used.

How can I know if my re-written expression is correct?

The best way to ensure your re-written expression is correct is to check it against the original expression and make sure they convey the same meaning. You can also have someone else review your re-written expression to provide feedback and catch any errors or inconsistencies.

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