Good graduate level QM text

[mjordan2nd]

Hello!

I just finished my undergraduate quantum mechanics education and am looking to self-study the next level some time soon (after finals!). We used Gasiorowicz in my class: a god-awful pedagogical text in my opinion. Though I've done pretty well in my course (I'm fairly certain I have an A), I feel like my understanding is severely lacking. What I'm looking for is a more in-depth treatment of quantum mechanics which spends a considerable amount of time on the mathematical formalism. Honestly, the math in quantum mechanics was way beyond anything we've learned at the undergraduate level, in my opinion. A bunch of hand-waving was used, and while I can solve quantum mechanics problems to a degree that my professor feels I'm worthy of an A, I'm afraid all I've learned are rules for symbolic manipulation without any real understanding of why those symbols are being manipulated as they are (for example: solving a differential equation involving operators). I've heard Sakurai and/or Shankar are the next logical steps. Any input from you guys would be appreciated.

[fss]

Sakurai/Shankar are probably the two most widely used texts for the first-year graduate level.

[dextercioby]

Sakurai and Shankar abound in mathematical hand-waving arguments...

I warmly reccomend to you the 2 volumes of Galindo and Pascual published in English by Springer. Softer maths in Ballentine's text, though.

[cbetanco]

Sakurai and Shankar abound in mathematical hand-waving arguments...


Ya, but that is how a lot of physics is done, by "hand-waving arguments" in the math. I think Shankar is very thorough in the physics, and it is really really well written. I personally would suggest Shankar, but that is mostly because it was what I used during graduate level QM, but also because I find other books too convoluted in the presentation, where Shankar actually speaks with surprising clarity.

[dextercioby]

True, but my answer was strictly addressing this part of the OP <What I'm looking for is a more in-depth treatment of quantum mechanics which spends a considerable amount of time on the mathematical formalism>. And I named the 2 Spanish authors.

[mjordan2nd]

I have definitely heard a lot about Sakurai and Shankar, and assume I will have to purchase one of those two at some point in the future, however this Galindo and Pascual book seems to be more what I am looking for at this point. The few reviews I can find about it rave about how good of a book it is. Thank you.

[deluks917]

http://www.amazon.com/Quantum-Mechanics-Mathematicians-Graduate-Mathematics/dp/0821846302

This book is a little unusual but might be nice to look at if you like to see things mathematically.

[dextercioby]

Takhtajan's text could be an option, if you're already familiar to advanced mathematics. G&P deal in 800 pages with a little more though, even if one could find things in it better dealt with in other books.

[Fredrik]

Consider getting a copy of "Lectures on quantum theory: mathematical and structural foundations (http://books.google.com/books?id=dVs8PcZ0Hd8C&lpg=PP1&pg=PP1#v=onepage&q&f=false)" by Chris Isham, in addition to whatever your first choice is. It's a short and easy to read book that focuses on what you need to understand the theory better.

[zahero_2007]

I recommend Cohen-tannoudje textbook it's a bit old but it is extremely good and very readable

[MathematicalPhysicist]

Cohen-Tannoudji is a great intermediate textbook in QM, but mainly for reference, I don't think you can learn from it without taking a course.

If the OP want's to delve into Quantum computers or chaos, there are recently published books by Rienhold Blumel's, which look nice.

His foundations textbook cover introductory quantum computing, and his advanced textbook covers the connection between classical and quantum, which is emmininet in nowadys quantum chaos.

[Daverz]

One book that tends to get overlooked is Arno Bohm's QM text (http://www.amazon.com/Quantum-Mechanics-Springer-Study-Arno/dp/0387953302/ref=sr_1_1?s=books&ie=UTF8&qid=1322869969&sr=1-1).

[zahero_2007]

Cohen-Tannoudji is a great intermediate textbook in QM, but mainly for reference, I don't think you can learn from it without taking a course.

If the OP want's to delve into Quantum computers or chaos, there are recently published books by Rienhold Blumel's, which look nice.

His foundations textbook cover introductory quantum computing, and his advanced textbook covers the connection between classical and quantum, which is emmininet in nowadys quantum chaos.

Why do you think so ? I'm learning from this book without taking a course as it explains things very well. The only disadvantage is that it doesn't have many exercises .

[aalaniz]

I felt like you mjordan2 thru undergrad and grad school.

Like others nothed, QM by Sakurai is good. I also like QM by Cohen-Tannoudji, Diu, and Laloe.

I actually posted a ~43 page doc at

http://www.physicsforums.com/showthread.php?t=553988

listing the books/literature/key math techniques/central physics ideas to feel like I was doing more than aping some voodoo prescription for calculating things.

Cheers,

Alex A.

[mjordan2nd]

Thank you for all of your kind responses. Now I have a tough decision to make. From the first two posts, Sakurai and/or Shankar does not seem like what I want to go with at the moment. Most likely I will end up using them for my graduate class anyway so I'd like to try something different for now. Galindo and Pascual seem to be rare, but have raving reviews where I can find them. If I can get my hands on the book, I may give that a try.

Quantum Mechanics for mathematicians seems to be a possibility as well. Again, reviews of this book are hard to come by, and from what I read on Amazon it may be slightly beyond my level at the moment. If I can find it at the library I will certainly check it out, though.

Isham seems to have pretty good reviews. I will check it out as soon as finals are over. Same with Cohen-tannoudje and Bohm.

Thanks all for the recommendations.

And Aalaniz, that looks like a fantastic little document, and I will look through it and get back to you. Thanks!

[MathematicalPhysicist]

zahero, as you said, not that many exercises, and its sheer size of both volumes can take quite alot of time to read from, this is why I said it's great as a reference, I used it quite alot in two courses in QM that I took.

[zahero_2007]

I agree that it is lengthy but I think that you can just read the chapters then read only the complements to the chapters that interests you. It's big because it has many complements to the chapters but you can skip alot of them.however the book is very readable and enjoyable to learn from

[dextercioby]

For exercises, you can always pick a book which has plenty, for example fully worked exercises (some of them can be through as part of the theory, not applications of it) you can find in the 2 volumes of Flügge.

[mjordan2nd]

I am definitely a fan of books with worked exercises. In my experience, when learning how to do quantum mechanics there is nothing more valuable than seeing quantum mechanics done. For this reason, Zetilli's book, and the Schaum's Outline on Quantum Mechanics were invaluable to me when taking this class.

[George Jones]

Consider getting a copy of "Lectures on quantum theory: mathematical and structural foundations (http://books.google.com/books?id=dVs8PcZ0Hd8C&lpg=PP1&pg=PP1#v=onepage&q&f=false)" by Chris Isham, in addition to whatever your first choice is. It's a short and easy to read book that focuses on what you need to understand the theory better.

I couldn't agree more with this. Every grad student should read this book.