Why Is Quantum Mechanics So Difficult? - Comments

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SUMMARY

This discussion centers on the pedagogical challenges of teaching Quantum Mechanics (QM), emphasizing the necessity of a mathematical foundation before introducing concepts. Participants advocate for a textbook like Ballentine's, which provides rigorous mathematical treatment, but note its graduate-level complexity. The conversation critiques the historical approach to QM education, suggesting it leads to misconceptions among students. Additionally, the importance of engaging teaching methods and the relevance of philosophical discussions in QM are debated.

PREREQUISITES
  • Understanding of Quantum Mechanics (QM) fundamentals
  • Familiarity with mathematical concepts such as Hilbert spaces and linear algebra
  • Knowledge of key QM texts, particularly Ballentine's and Griffiths' books
  • Awareness of the historical context of QM development
NEXT STEPS
  • Explore "Ballentine's Quantum Mechanics" for a rigorous mathematical approach
  • Investigate "Griffiths' Introduction to Quantum Mechanics" for a more conceptual understanding
  • Study the derivation of the Stefan-Boltzmann law in statistical mechanics
  • Research different pedagogical methods for teaching Quantum Mechanics effectively
USEFUL FOR

Physics educators, undergraduate students in physics, and anyone interested in improving their understanding of Quantum Mechanics and its teaching methodologies.

  • #241
Didnt Hawking famously say - every equation he puts in a book takes X amount of sales off.

Paraphrased.
 
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  • #242
Supposedly, it's absolutely impossible to put the equations of modern physics into plain English. I don't buy that. Has any group of physicists ever even attempted to "Gutenbergize" QM for the public?
 
  • #243
I believe that would be most uncompelling and ugly.
 
  • #244
bhobba said:
Then get copy of Landau - Mechanics where all of Classical mechanics is derived from this alone

For something worthy of this honor, it would need to be fully consistent with the applicable regimes of Newton, Hamilton, Lagrange, Schrödinger, Heisenberg, Einstein (at least as far as SR), and also all the various types of material physics. And on top of all that, it also has to be profinite, so it can be put to practical use.

Are you saying that the path integral is up to that challenge?
 
  • #245
houlahound said:
I believe that would be most uncompelling and ugly.

Sic transit gloria. You have a better idea?
 
  • #246
Yes, learn the math and see the beauty in full.
 
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  • #247
houlahound said:
Didnt Hawking famously say - every equation he puts in a book takes X amount of sales off.

Paraphrased.
That's valid for popular science books. For textbooks on physics the opposite is true: The more formulae the author offers, the more steps are made explicit in a derivation, for the student the more simple it is to follow and understand the argument ;-).
 
  • #248
houlahound said:
Yes, learn the math and see the beauty in full.

There's nothing beautiful about having to observe everything projected onto a random choice among real-valued probabilities. But that's how the actual world works, and that's the mystery the public wants to understand.
 
  • #249
Define understand and how you know you understand something.

Personally I think the word understand is vague and rather useless.
 
  • #250
houlahound said:
Define understand and how you know you understand something.

As far as explaining physics to the public, I'd define understanding as a form of economic utility. Math is the only reliable way to grapple with the "Big Questions". If people are to expend time, money, and effort to learn mathematical physics, they expect to see how that's done. If that's not what they see promoted, they'll take the low road and learn nothing or less.
 
  • #251
Explaining equations in plain English does not mean there are no more equations. It means that the equations are written to be teaching tools themselves, rather than merely something to learn. I never thought it possible, but apparently they've been there for quite a while, hidden beneath a pile of Google trolls, and now the trolls have disappeared. (Obama's parting gift?) Here's an example:
http://www.imperial.ac.uk/media/imp...issertations/2012/Alec-Owens-Dissertation.pdf

I suppose you think this math is ugly?
 
  • #252
Why should this be ugly?
 
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