Book recommendation: Mathematical treatment

In summary: Can you reccomend any other text similar to Sudbery's that is still more group theoretic than Prugovecki? Sudbery seems to be out of print, I saw a copy of it going for $600 on half.com!Just a question about Prugovecki-- this is what the description says:A rigorous, critical presentation of the basic mathematics of nonrelativistic quantum mechanics, this text is suitable for courses in functional analysis at the advanced undergraduate and graduate levels.So am I right in assuming that this is a book on the mathematics that is used in quantum mechanics? Or does it introduce the mathematics and the quantum mechanics?I've had linear algebra, functional
  • #1
cliowa
191
0
I'm looking for a book on Quantum Mechanics on an introductory level (concerning the physics), which is fairly advanced concerning the mathematics (i.e. some book that does not praise as a mathematical revolution that there actually is something called a dual space to some vector space). Do you have any recommendations?

Best regards and thanks in advance...Cliowa
 
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  • #2
cliowa said:
I'm looking for a book on Quantum Mechanics on an introductory level (concerning the physics), which is fairly advanced concerning the mathematics (i.e. some book that does not praise as a mathematical revolution that there actually is something called a dual space to some vector space). Do you have any recommendations?

Best regards and thanks in advance...Cliowa

You might want to look at Quantum Mechanics and the Particles of Nature: An Outline for Mathematicians by Anthony Sudbery. This book was written for final-year British mathematics students. This book, unlike many physics books, has nice, crisp mathematics, but it does not dwell on mathematics, so it might (Edit: Yikes, I left out the word "not".) be what you're looking for. I quite like this book.

Another possibility is https://www.amazon.com/dp/0486453278/?tag=pfamazon01-20, which does a lot more functional analysis (and less group theory) than does Sudbery.
 
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  • #3
  • #4
George Jones said:
You might want to look at Quantum Mechanics and the Particles of Nature: An Outline for Mathematicians by Anthony Sudbery. This book was written for final-year British mathematics students. This book, unlike many physics books, has nice, crisp mathematics, but it does not dwell on mathematics, so it might (Edit: Yikes, I left out the word "not".) be what you're looking for. I quite like this book.

Another possibility is https://www.amazon.com/dp/0486453278/?tag=pfamazon01-20, which does a lot more functional analysis (and less group theory) than does Sudbery.

Wow, thanks for those two links, they look quite promising. In fact, I already had a llook at Prugovecki, and I have to admit I like it quite alot. Thanks again.
 
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  • #5
Hurkyl said:
If you follow the "links" link at the top of the site, you will eventually come to this site:

http://www.lorentz.leidenuniv.nl/modphys/

That is a good link, thank you very much. I wasn't aware of the existence of this set of notes.
 
  • #6
George Jones said:
You might want to look at Quantum Mechanics and the Particles of Nature: An Outline for Mathematicians by Anthony Sudbery. This book was written for final-year British mathematics students. This book, unlike many physics books, has nice, crisp mathematics, but it does not dwell on mathematics, so it might (Edit: Yikes, I left out the word "not".) be what you're looking for. I quite like this book.

Another possibility is Prugovecki, which does a lot more functional analysis (and less group theory) than does Sudbery.

Can you reccomend any other text similar to Sudbery's that is still more group theoretic than Prugovecki? Sudbery seems to be out of print, I saw a copy of it going for $600 on half.com!
 
  • #7
Just a question about Prugovecki-- this is what the description says:
A rigorous, critical presentation of the basic mathematics of nonrelativistic quantum mechanics, this text is suitable for courses in functional analysis at the advanced undergraduate and graduate levels.
So am I right in assuming that this is a book on the mathematics that is used in quantum mechanics? Or does it introduce the mathematics and the quantum mechanics?
I've had linear algebra, functional analysis and am currently learning Lie algebras and partial differential equations, so I'm looking for some sort of an introduction to quantum mechanics that presupposes the student is comfortable with rigorous mathematics (Or atleast, analysis and algebra) assumes no quantum background.
I've heard Mackey is good in that regard.
Does anyone have any input? Is Prugovecki such a book?
I heard that Landau's book is good, but is it rigorous in the mathematical sense? (i.e. is everything justified in a logical manner?)
Thanks.
 

1. What is a "mathematical treatment" in relation to books?

A mathematical treatment in books refers to the use of mathematical concepts, equations, and formulas to explain and solve problems in a specific subject or field.

2. What types of books typically contain a mathematical treatment?

Books that contain a mathematical treatment can vary in subject, but they often include textbooks, research papers, and academic publications in fields such as mathematics, physics, engineering, and economics.

3. How can a mathematical treatment enhance a book's content?

A mathematical treatment can enhance a book's content by providing a more comprehensive and precise explanation of concepts, allowing for more accurate analysis and problem-solving, and providing a deeper understanding of the subject matter.

4. Are there any prerequisites for understanding a book with a mathematical treatment?

The prerequisites for understanding a book with a mathematical treatment will vary depending on the subject and level of the book. Generally, a strong foundation in basic mathematical concepts and understanding of the subject matter is recommended.

5. Are there any resources available to help with understanding a book with a mathematical treatment?

Yes, there are many resources available to help with understanding a book with a mathematical treatment. These can include study guides, online tutorials, and additional practice problems. It can also be helpful to consult with a teacher, tutor, or fellow mathematician for further clarification.

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