Is this a typo? (Quantum Theory for Mathematicians by Brian C. Hall)

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Discussion Overview

The discussion revolves around a potential typographical error in the book "Quantum Theory for Mathematicians" by Brian C. Hall, specifically regarding the notation of charge variables. Participants are exploring the implications of this notation within the context of quantum physics and its mathematical representation.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant identifies what they believe to be a typo, suggesting that "e" should actually be "Q" since "e" was not previously introduced.
  • Another participant agrees that mathematically, one could infer that ##Q^2 = e^2##, leading to ##Q=e## or ##Q=-e##, but emphasizes that the context of physics requires clarity in variable notation.
  • Concerns are raised about whether "Q" and "e" have different conventional meanings in physics, with some participants noting that "Q" is often used generically for charge while "e" specifically refers to the charge of an electron.
  • There is a suggestion that the author may have inconsistently switched between using "Q" and "e" in the text.
  • One participant warns that "e" typically denotes the charge of a proton, while the charge of an electron is represented as ##Q_{\text{e}}=-e##, indicating variability in notation across different texts.
  • A later post questions the absence of Coulomb's constant in a specific equation, suggesting a classical physics context.
  • Another participant speculates that Coulomb's constant may be set to 1 in appropriate units.

Areas of Agreement / Disagreement

Participants express differing views on the notation of charge, with no consensus reached on whether the observed discrepancy is a typo or a matter of varying conventions in physics. The discussion remains unresolved regarding the implications of these notational differences.

Contextual Notes

There are limitations in the discussion regarding the assumptions made about variable notation and the context in which these symbols are used, as well as the potential for different interpretations based on varying conventions in physics literature.

danielristic
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TL;DR
Just started reading this book and wondering if this is a typo or if I'm already lost.
Hello,

After reading a few vulgarisation books, I'm looking into familiarising myself with the more mathematical aspects of quantum physics so I've started reading Quantum Theory for Mathematicians by Brian C. Hall.

I'm only 9 pages in but I've already spotted what I think is a typo. I checked online and the author is providing some corrections but this one is not part of the list.

Here's the relevant except:

Hall_2013_pdf__page_26_of_566_.png


As "e" was never introduced I'm assuming this is really "Q", what do you think?
 
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danielristic said:
Summary:: Just started reading this book and wondering if this is a typo or if I'm already lost.

Hello,

After reading a few vulgarisation books, I'm looking into familiarising myself with the more mathematical aspects of quantum physics so I've started reading Quantum Theory for Mathematicians by Brian C. Hall.

I'm only 9 pages in but I've already spotted what I think is a typo. I checked online and the author is providing some corrections but this one is not part of the list.

Here's the relevant except:

View attachment 259386

As "e" was never introduced I'm assuming this is really "Q", what do you think?
Assuming you are a mathematician, can't you prove from those equations that ##Q = \pm e##?
 
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From a mathematical standpoint, given the last two equations sure, you can infer that ##Q^2 = e^2## and that therefore ##Q=e## or ##Q=-e## but I'm not trying to solve a maths problem here. In physics, variables are attached to measurable quantities or constants and conventional notations tend to use the same symbols to designate the same things.

I don't have an extensive background in physics but I know that ##e## is commonly used for the charge of an electron but the previous except states "Q is the charge of the electron" so I was just trying to figure out if Q and e had a different conventional meaning for physicists or if it was simply a typographical error.
 
danielristic said:
From a mathematical standpoint, given the last two equations sure, you can infer that ##Q^2 = e^2## and that therefore ##Q=e## or ##Q=-e## but I'm not trying to solve a maths problem here. In physics, variables are attached to measurable quantities or constants and conventional notations tend to use the same symbols to designate the same things.

I don't have an extensive background in physics but I know that ##e## is commonly used for the charge of an electron but the previous except states "Q is the charge of the electron" so I was just trying to figure out if Q and e had a different conventional meaning for physicists or if it was simply a typographical error.
It certainly looks like he suddenly decided to use ##e## instead of ##Q## and then immediately changed his mind again!

From what I know, ##Q## is generally used as a generic symbol for the charge of anything. And, ##e## is often used specifically as the charge on an electron; or as minus the charge on an electron, i.e. the charge on a proton, depending on the author.
 
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I see, makes sense. Thanks!
 
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danielristic said:
From a mathematical standpoint, given the last two equations sure, you can infer that ##Q^2 = e^2## and that therefore ##Q=e## or ##Q=-e## but I'm not trying to solve a maths problem here. In physics, variables are attached to measurable quantities or constants and conventional notations tend to use the same symbols to designate the same things.

I don't have an extensive background in physics but I know that ##e## is commonly used for the charge of an electron but the previous except states "Q is the charge of the electron" so I was just trying to figure out if Q and e had a different conventional meaning for physicists or if it was simply a typographical error.
Be careful. Usually ##e## is the charge of the proton (positive). An electron then has charge ##Q_{\text{e}}=-e## (negative), but some textbooks/papers may use a different notation.
 
Why is there no Coulomb's constant in (1.3)?

Btw, AFAIK this is all classical physics.
 
I suppose that is because, "in appropriate units", ##K=1##
 
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