Robert_G
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Hi. I am reading a book entitled "Atom-Photon interactions" by Claude Cohen-Tannoudji, et al.
There is a symbol which looks like [itex]\mathscr{P}[/itex]. The authors state that this symbol stands for the principle part. e.g.
[itex]\hat{\Delta}_b(E)=\frac{1}{2\pi} \mathscr{P} \int dE' \frac{\hat{\Gamma}_b(E')}{E-E'}[/itex]
Principle part usually refers to the negative-power portion of the Laurent series of a function. Now in the above equation, is it true that we need to expand the right hand side of the equation into Laurent series, and only take the negative-power portion from it?
In the context of this book, I have a strong feeling that [itex]\mathscr{P}[/itex] just means [itex]E\neq E'[/itex].
Are you familiar with the definition of the principle part? Please tell me.
There is a symbol which looks like [itex]\mathscr{P}[/itex]. The authors state that this symbol stands for the principle part. e.g.
[itex]\hat{\Delta}_b(E)=\frac{1}{2\pi} \mathscr{P} \int dE' \frac{\hat{\Gamma}_b(E')}{E-E'}[/itex]
Principle part usually refers to the negative-power portion of the Laurent series of a function. Now in the above equation, is it true that we need to expand the right hand side of the equation into Laurent series, and only take the negative-power portion from it?
In the context of this book, I have a strong feeling that [itex]\mathscr{P}[/itex] just means [itex]E\neq E'[/itex].
Are you familiar with the definition of the principle part? Please tell me.