Playing around with summations

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Discussion Overview

The discussion revolves around the concept of summations, specifically the sum of the series Ʃn^n in the context of quantum optics and its relation to the Q function. Participants explore the meaning of 'average' values in this context and seek clarification on the implications of these terms.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant seeks an explanation for the assertion that the sum from 0 to infinity Ʃn^n equals 1, questioning the role of 'average' values in this context.
  • Another participant asks for clarification on what is meant by 'average values' and whether n is independent of itself in the summation.
  • A different participant suggests that the index of the sum applies only to the power and not to the average value, indicating that summing over the average photon number may not be meaningful.
  • A participant provides a link to a specific page in a book for further context regarding the Q function and its application in quantum optics.
  • One participant later indicates they have resolved their confusion without further elaboration.

Areas of Agreement / Disagreement

The discussion contains multiple viewpoints regarding the interpretation of the summation and the concept of average values. No consensus is reached on the implications of these terms or the validity of the initial claim.

Contextual Notes

Participants express uncertainty about the definitions of 'average' values and how they relate to the summation. There is also a lack of clarity on the mathematical steps involved in the assertion made in the literature.

Hazzattack
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Hi guys, I'm hoping someone could explain this for me... and was also hoping that some decent literature could be suggested to help me get more comfortable with series expansions of things etc...

So i was playing around with the Q function (its used in quantum optics) and in the book they say that;

For the sum from 0 to infinity Ʃn^n = 1

(the bold case n's represent 'average' values - not sure if that makes a difference?)

Why is this the case ?

Thanks to anyone who can shed some light on this.
 
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Can you explain what you mean by average values? Is n totally independent of n here?
 
I think the index of the sum only applies to the power and not to the average value. (which i think is what you mean by them being independent?

In this case the sum represents the photon distribution where n represents the average photon number, so I'm assuming it doesn't make sense to sum over that?

Sorry if that isn't very clear...
 
Never mind I've realized why. Thanks for anyone who took a look.
 

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