Book recommendation: Mathematical treatment

[cliowa]

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

 

[George Jones]

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.

 

[Hurkyl]

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/

 

[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.

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 a lot. Thanks again.

 

[cliowa]

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.

 

[InbredDummy]

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 recommend 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!

 

[Pseudo Statistic]

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.