Math Methods for Quantum Mechanics (QM) Prerequisites

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Discussion Overview

The discussion revolves around the suitability of specific mathematical textbooks as prerequisites for studying quantum mechanics (QM). Participants explore the relevance of Kreyszig's book on functional analysis and Hassani's texts, considering their content and intended audience.

Discussion Character

  • Debate/contested
  • Technical explanation

Main Points Raised

  • Some participants suggest that Hassani's book is sufficient for practical applications in QM, while others express uncertainty about Kreyszig's relevance.
  • One participant notes that Kreyszig's chapters 10 and 11 are valuable for understanding the mathematical foundations of QM, emphasizing the importance of unbounded operators on Hilbert spaces.
  • There is a distinction made between the two books: Hassani is seen as more practical for theoretical physicists who approach mathematics like engineers, whereas Kreyszig is viewed as more rigorous and suited for those who approach it like mathematicians.
  • Participants inquire about which specific book by Hassani is being referenced, as he has multiple texts on mathematical physics and methods.
  • One participant mentions that Kreyszig has also authored a practical mathematics book, Advanced Engineering Mathematics, which may be more comparable to Hassani's works.

Areas of Agreement / Disagreement

Participants express differing views on the adequacy of Kreyszig and Hassani's books for QM prerequisites, with no consensus reached on which is more appropriate or sufficient.

Contextual Notes

Some participants highlight that the choice of textbook may depend on the depth of mathematical formalism desired in QM, indicating a lack of clarity on the specific requirements for different approaches to the subject.

Jianphys17
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Hi, people
I wondered if as prerequisites for QM, the Kreyszig (for func. analysis) and Hassani's book they be suffices ..
Thank you in advance !
 
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It depends how deep you want to go in the mathematical formalism of QM, but Hassani is more than enough to go quite far. I don't know the Kreyszig book.
 
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Jianphys17 said:
Hi, people
I wondered if as prerequisites for QM, the Kreyszig (for func. analysis) and Hassani's book they be suffices ..
Thank you in advance !
Kreyszig's book on functional analysis is very good. Chapters 10 and 11 will serve you well as an introduction to the mathematical underpinnings of QM. Should you choose another title, be sure it contains a good discussion of unbounded operators on Hilbert spaces. I don't know the Hassani book.
 
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Hassani and Kreyszig are very different books, serving very different purposes.

Hassani contains more or less all mathematics that a practical theoretical physicist may need in practical calculations.
Kreyszig is a book specialized in functional analysis, which is not so much needed in practical calculations in physics, but is needed for a mathematically rigorous formulation of quantum mechanics.

There are two kinds of theoretical physicists, those who use mathematics more like engineers and those who use mathematics more like mathematicians. Hassani is for the former kind of physicists, Kreyszig is for the latter.
 
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Krylov said:
Kreyszig's book on functional analysis is very good. Chapters 10 and 11 will serve you well as an introduction to the mathematical underpinnings of QM. Should you choose another title, be sure it contains a good discussion of unbounded operators on Hilbert spaces. I don't know the Hassani book.

Which book by Hassani are you talking about? He has one on mathematical physics and another one on mathematical methods.
 
noir1993 said:
Which book by Hassani are you talking about? He has one on mathematical physics and another one on mathematical methods.
I wasn't the one that brought up Hassani, the OP did, so maybe he can answer your question. I do not know his book(s).
 
Krylov said:
I wasn't the one that brought up Hassani, the OP did, so maybe he can answer your question. I do not know his book(s).

I replied to the wrong comment. My bad!

Jianphys17 said:
Hi, people
I wondered if as prerequisites for QM, the Kreyszig (for func. analysis) and Hassani's book they be suffices ..
Thank you in advance !

So, if your are talking about Hassani's textbook on mathematical physics, it's more than sufficient, not just for quantum mechanics but several other topics as well.
 
noir1993 said:
I replied to the wrong comment. My bad!
So, if your are talking about Hassani's textbook on mathematical physics, it's more than sufficient, not just for quantum mechanics but several other topics as well.
Yes, The math physics book !
 
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