Next-Level Quantum Mechanics: A Guide for Graduate Students

In summary: I'm not entirely sure what level I will graduate to yet. As for the other two texts, Takhtajan's and G&P, I am not familiar with them yet. I will definitely be looking into them soon.
  • #1
mjordan2nd
177
1
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.
 
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  • #2
Sakurai/Shankar are probably the two most widely used texts for the first-year graduate level.
 
  • #3
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.
 
  • #4
dextercioby said:
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.
 
  • #5
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.
 
  • #6
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.
 
  • #8
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.
 
  • #10
I recommend Cohen-tannoudje textbook it's a bit old but it is extremely good and very readable
 
  • #11
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.
 
  • #13
MathematicalPhysicist said:
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 .
 
  • #14
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

https://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.
 
  • #15
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!
 
  • #16
zahero, as you said, not that many exercises, and its sheer size of both volumes can take quite a lot of time to read from, this is why I said it's great as a reference, I used it quite a lot in two courses in QM that I took.
 
  • #17
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 a lot of them.however the book is very readable and enjoyable to learn from
 
  • #18
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.
 
  • #19
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.
 
  • #20
Fredrik said:
Consider getting a copy of "Lectures on quantum theory: mathematical and structural foundations" 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.
 

1. What is a good graduate level quantum mechanics text?

A good graduate level quantum mechanics text is one that provides a thorough and comprehensive understanding of the subject matter, while also being accessible and engaging for students. It should cover the fundamental principles and mathematical techniques of quantum mechanics, and also include real-world applications and examples. Additionally, a good textbook should have clear and concise explanations, helpful diagrams and illustrations, and practice problems for students to test their understanding.

2. What are the key topics that should be covered in a graduate level QM text?

The key topics that should be covered in a graduate level quantum mechanics text include the postulates of quantum mechanics, wave-particle duality, the Schrödinger equation, operators and observables, quantum states and probabilities, and time evolution. Other important topics may include the harmonic oscillator, angular momentum, and the hydrogen atom. Depending on the level of the course, the text may also cover more advanced topics such as quantum entanglement, quantum field theory, and applications in condensed matter physics and quantum computing.

3. Are there any recommended textbooks for graduate level quantum mechanics?

Yes, there are many recommended textbooks for graduate level quantum mechanics, including "Introduction to Quantum Mechanics" by David J. Griffiths, "Quantum Mechanics: 500 Problems with Solutions" by G. Aruldhas, and "Quantum Mechanics" by Claude Cohen-Tannoudji. Ultimately, the best textbook will vary depending on the individual student's learning style and the specific course requirements.

4. How does a good graduate level QM text differ from an undergraduate level QM text?

A good graduate level quantum mechanics text will typically go into more depth and detail than an undergraduate level text. It may also cover more advanced topics and require a higher level of mathematical rigor. Additionally, a graduate level text may place a greater emphasis on real-world applications and examples, rather than just theoretical concepts. Furthermore, a graduate level text may assume a higher level of prior knowledge, such as a strong background in calculus and linear algebra.

5. What makes a good graduate level QM text challenging?

A good graduate level quantum mechanics text can be challenging due to its complex subject matter and mathematical concepts. In addition, the abstract nature of quantum mechanics can be difficult for students to grasp, and the probabilistic nature of quantum systems can be counterintuitive. Furthermore, the advanced topics covered in a graduate level text may require a strong understanding of foundational principles and a high level of critical thinking and problem-solving skills.

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