Recommended Quantum Physics and Maths book?

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Discussion Overview

The discussion revolves around recommendations for books on advanced mathematics and physics topics, specifically focusing on Lagrangian and Hamiltonian mechanics, Fourier transforms, differential equations, Gaussian functions, surface integrals, quantum mechanics, and relativity. The scope includes both theoretical and practical applications suitable for a high school student with some prior knowledge in these areas.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Homework-related

Main Points Raised

  • One participant expresses a desire for book recommendations on advanced topics in mathematics and physics, indicating a background in basic calculus and first-year university-level material.
  • Another participant cautions that the subjects mentioned are advanced and suggests that a solid foundation in basic mathematics and physics is essential before tackling such topics.
  • A subsequent post reiterates the caution about the advanced nature of the subjects and emphasizes the importance of understanding calculus.
  • A participant provides two book recommendations: Braun's "Differential Equations and their Applications" and Holland's "Applied Analysis by the Hilbert Space Method," noting their non-standard approaches and relevance to quantum mechanics.
  • The same participant mentions removing a third book suggestion without indicating its quality, citing a desire to step away from the forums.

Areas of Agreement / Disagreement

There is a disagreement regarding the appropriateness of diving into advanced topics at the high school level. Some participants advocate for a more foundational approach, while others support the pursuit of advanced materials given the original poster's prior knowledge.

Contextual Notes

Participants have varying levels of experience and knowledge, which influences their perspectives on the suitability of advanced texts for a high school student. The discussion does not resolve the question of whether the recommended books are appropriate for the original poster's level.

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Hi, I'm currently in high school but I know several university maths and physics (just a little)
I want to know about

Maths:
Lagrangian and Hamiltonian
Fourier Transform (I self-studied Fourier series)
Differential Equations (only know one way to solve them, I think its the most basic one)
Gaussian Function and its properties (like multiplying two of them and making a one with a p I couldn't find anything related to it online)
Surface Integrals and more on integrals (like Cantor Integrals)

Physics:
Quantum Mechanics(I've learned the basics so I want something that's understandable (with proofs would be nice) but not too easy but then not too hard as well. So I guess I want introductory Quantum Mechanics Book with a little rigor)
Relativity: Understandable one with a lot of contents (exercise questions too)

If anyone could find a good book please let me know.
Thanks in advance
 
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Those are pretty advanced subjects. If you are only in high school I would suggest that it would be more beneficial to gain a firm grounding in your maths and physics from the basics up than to jump straight into a book about Lagrangians or differential equations. A thorough understanding of calculus is necessary.
 
I did do a lot of basic calculus and did year one university mathematics and physics is that okay?
 
KSG4592 said:
Those are pretty advanced subjects. If you are only in high school I would suggest that it would be more beneficial to gain a firm grounding in your maths and physics from the basics up than to jump straight into a book about Lagrangians or differential equations. A thorough understanding of calculus is necessary.

Forgot to press 'reply'
 
Try these if you like. I definitely prefer non-standard books, I dislike the ascetic quality that many modern books have.

1. Braun, "Differential Equations and their Applications". Looks like it covers a lot and rigorously but not in the standard way.
2. Holland, "Applied Analysis by the Hilbert Space Method". Looks quirky and very relevant for the modern QM.

I've removed the third suggestion I had here, it's not because I think it was a bad book to choose but I want to step away from these forums for a while and this is a good time to do it. These two seem to fit what you requested very nicely and I leave it up to you which books you want to buy.
 
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