Functional analysis, and Quantum Mechanics

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Discussion Overview

The discussion revolves around the relationship between functional analysis and theoretical quantum physics, particularly whether studying functional analysis can enhance understanding of quantum mechanics. Participants share their experiences and perspectives on the relevance and rigor of the course content.

Discussion Character

  • Exploratory, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant expresses interest in taking an introductory course in functional analysis to better understand theoretical quantum physics.
  • Another participant believes that functional analysis is beneficial, citing their reading of QED and a brief introduction to calculus of variations.
  • A participant mentions that their university no longer offers calculus of variations, indicating a potential gap in available coursework.
  • There is a question about the mathematical rigor of the functional analysis course, with concerns that it may not be as rigorous as courses designed specifically for mathematicians.
  • One participant shares their experience of taking a functional analysis course that seemed unrelated to quantum mechanics, suggesting a disconnect between the two subjects.
  • A later reply comments on the cultural differences between mathematics and physics, implying that understanding the connections requires navigating the boundaries between the two fields.

Areas of Agreement / Disagreement

Participants express differing views on the relevance of functional analysis to quantum mechanics, with some believing in its value while others see little connection. The discussion remains unresolved regarding the course's rigor and its applicability to quantum physics.

Contextual Notes

Participants have varying backgrounds in mathematics and physics, which may influence their perspectives on the relationship between functional analysis and quantum mechanics. There are mentions of specific courses and their availability, which could affect the discussion's context.

malawi_glenn
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Hi!

I was thinking about taking an introductory course in Functional analysis the commming spring, and was wondering if you more experienced guys can tell me if this is a good complement to understand theoretical quantum physics better?

Cheers
 
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I think so, but I'm going off reading QED plus a very brief introduction to calculus of variations.
 
They are not offering Calculus of variations anymore at my University =(
 
what math courses have you taken already?
 
is this course mathematically rigorous?
i.e given by mathematicians for mathmematicians (and those who inclined to rigorous maths).
cause as i know it in QM courses and physics in general you already given the maths needed (with shaken mathematical foundations), because i myself as a maths/physics student as any maths/physics student knows we first learn the maths in the physics courses which are needed and after some semesters or a few weeks we learn it in the specific maths course.
so i guess i myself first will learn QM and the maths used there in a physics course and afterwards i will learn the maths needed rigorously.
if you are a maths/physics major you'll know what I am talking about.
 
I took a course on functional analysis last spring, and it nearly didn't have anything to do with the QM. It dealt with completely different kind of things, or at least I cannot see the connection yet.
 
Maths and physics are like different cultures. Stick to the boundary of the two and the connections will be more apparent unlike you are a genuis.
 

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