Next step up from Shankar

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In about a month or perhaps less I believe I will have finished my reading of Shankar. Which textbooks would you consider to be a next step from that? There are 3 things I would appreciate. One is slightly more mathematical rigour, perhaps something that makes greater use of methods from functional analysis to ground the math used. The lack of coverage of rigged Hilbert spaces in Shankar kind of confused me about what you can and what you can't do and why. Another thing would probably be more applications. Finally, I'd like something with more problems, I wasn't very satisfied with the problems in Shankar. They were scattered all over the place, and there were too few.
 
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  • #2
Ssnow
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"Functional Analysis, Sobolev Spaces and Partial Differential Equation." of Haim Brezis

Ssnow
 
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"Functional Analysis, Sobolev Spaces and Partial Differential Equation." of Haim Brezis

Ssnow
That's not really a QM book, more of a functional analysis book, but it IS the recommended book for my uni and I'm gonna get it for free next year!
 
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I am looking for a QM book tho.
 
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There is a textbook, Quantum Physics, by Glimm and Jaffe, but on browsing it, it looks like this may be too much unless you are interested in a career in this area.

Many universities use Sakurai, but they do not use Shankar. After reading Shankar, I felt that perhaps the best strategy is to use Shankar for the first semester, up to say chapter 4 and then shift to Sakurai. Since I started Quantum mechanics in the mid 70's and maybe before, my quantum teachers always taught from their notes and gave many textbooks as references. It seems like they felt there was no one book that they were comfortable on all topics.

Merzbacher has many quantum physics problems. Messiah may be good, perhaps a little dated.

I think maybe quantum mechanics from the Greiner series is good. I cannot remember if Greiner is the author or the series but google might shed some light.
 
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dextercioby
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Nonrelativistic Quantum Mechanics by A. Capri has all the useful matters and goes into the functional analytical foundation of Quantum Mechanics. A more mathematical treatment is in the two volumes of Galindo & Pascual or in the "bible-like" book by Manoukian.
 
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There is a textbook, Quantum Physics, by Glimm and Jaffe, but on browsing it, it looks like this may be too much unless you are interested in a career in this area
I kind of am, though I'm not sure yet.
 
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DrClaude
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I think maybe quantum mechanics from the Greiner series is good. I cannot remember if Greiner is the author or the series but google might shed some light.
Greiner is good, especially on the mathematical side.

I suggest Sakurai and Napolitano as the next step.
 
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Hi @AndreasC , I know that it is not a QM book, my suggestion regard the math tools you need for quantum mechanics, from a point of view of a mathematician this book of Functional Analysis is fundamental in order to understand the QM and some results are true also for Hilbert space. Moreover I think this volume can clarify your dubts on Hilbert spaces. Anyway if you prefer a physical approach with a different language I suggest you an alternative book: " Quantum Mechanics: Concepts and Applications " Nouredine Zettili, ed. Wiley. Ssnow
 
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If you want a book on the mathematical foundations, I'd recommend one which uses the "rigged Hilbert space approach" which is the physicists' Hilbert space used in non-relativistic QM of a fixed number of particles made rigorous. My favorite is the two-volume book by Galindo&Pascual:

A. Galindo, P. Pascual, Quantum Mechanics, Springer Verlag, Heidelberg (1990), 2 Vols.

Online are also nice reviews, e.g.,

R. de la Madrid, Quantum Mechanics in rigged Hilbert space language, Dissertation, Uni. de Valladolid
http://galaxy.cs.lamar.edu/~rafaelm/webdis.pdf
 
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If you want a book on the mathematical foundations, I'd recommend one which uses the "rigged Hilbert space approach" which is the physicists' Hilbert space used in non-relativistic QM of a fixed number of particles made rigorous. My favorite is the two-volume book by Galindo&Pascual:

A. Galindo, P. Pascual, Quantum Mechanics, Springer Verlag, Heidelberg (1990), 2 Vols.

Online are also nice reviews, e.g.,

R. de la Madrid, Quantum Mechanics in rigged Hilbert space language, Dissertation, Uni. de Valladolid
http://galaxy.cs.lamar.edu/~rafaelm/webdis.pdf
Someone else also recommended this, I'll definitely check it out!
 

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