Rigor in Quantum physics -- Do I need to know Functional Analysis well?

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Discussion Overview

The discussion revolves around the necessity of understanding functional analysis in the context of quantum physics. Participants explore whether rigorous knowledge of functional analysis is essential for studying quantum mechanics, considering both theoretical and practical perspectives.

Discussion Character

  • Debate/contested

Main Points Raised

  • One participant questions the necessity of knowing functional analysis well to handle quantum physics effectively.
  • Another suggests using quantum physics as motivation to study functional analysis.
  • A participant expresses interest in the strict necessity of functional analysis for quantum mechanics.
  • Some participants argue that functional analysis is not necessary for most physicists, including Nobel laureates, who may not engage deeply with rigorous functional analysis.
  • It is noted that there are specific areas of active research, such as quantum chaos, where functional analysis may be useful.
  • One reply recommends that while functional analysis is not required for quantum mechanics, it could be beneficial to explore applied functional analysis in conjunction with quantum mechanics.
  • A participant states that introductory quantum physics is primarily based on electromagnetism.

Areas of Agreement / Disagreement

Participants express differing views on the necessity of functional analysis for quantum physics. While some argue it is not essential, others suggest it could be beneficial, indicating a lack of consensus on the topic.

Contextual Notes

The discussion reflects varying levels of engagement with functional analysis among participants, highlighting the potential for different educational paths in physics and mathematics.

Jianphys17
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Hello, I've a following question:
Is necessary know well func. analysis, and all its theorems to handle well quantum physics...?
 
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Use quantum physics to inspire study of func. o:)
 
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Likes   Reactions: S.G. Janssens
Okay, but I'm interested in knowing if it's strictly necessary (for QM) ...:oldconfused:
 
No, it is not necessary if you are only interested in physics. Most quantum physicists, even Nobel prize winners, do not use much of rigorous functional analysis.
 
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Likes   Reactions: Jianphys17
There are some odd corners of active research where it can be useful deep in the theoretical end. (Quantum chaos, for example.) But no, you won't need it in typical undergraduate and graduate course sequences.
 
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Likes   Reactions: fisher garry
To the OP:

I read in your profile that you like both mathematics and physics. So, although from a physicist's point of view, FA is not required knowledge for QM, I would still recommend that at some point you take a look at an applied FA book with some discussion of QM. Vice versa, I would recommend every mathematics student of FA ("pure" or "applied", it does not matter) to take a look at a book on theoretical QM. The birth of the two subjects roughly coincides in time, their development is strongly correlated and you may enjoy seeing this for yourself.
 
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Likes   Reactions: fisher garry, Jianphys17, Dr. Courtney and 1 other person
Most of the introductionary quantum physics is based on electromagnetism according to me.
 

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