How to start with advanced quantum mechanics

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Discussion Overview

The discussion centers on recommendations for advancing in quantum mechanics after completing an introductory course. Participants explore various resources, including textbooks and online courses, that could facilitate deeper understanding of concepts such as Heisenberg Matrix Mechanics and the Hilbert space approach to quantum theory.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant suggests starting with Merzbacher and R. Shankar after completing a year-long course in quantum mechanics.
  • Another participant recommends Ballentine's book, supplemented by Shankar's work.
  • A third participant supports the recommendation of Ballentine and suggests reading Isham beforehand for better comprehension, noting that "matrix mechanics" is considered an obsolete term.
  • A different participant recommends online courses by Prof. V. Balakrishnan, highlighting his ability to explain Hilbert Space concepts effectively.

Areas of Agreement / Disagreement

Participants generally agree on the value of Ballentine's book, but there are differing opinions on supplementary materials, with some advocating for Isham and others for online courses. The discussion remains unresolved regarding the best starting point for advanced quantum mechanics.

Contextual Notes

There is an implicit assumption that participants have a foundational understanding of quantum mechanics, and the discussion does not resolve the historical context of matrix mechanics versus Hilbert space approaches.

dekajyo
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Hey, I did a full year course on quantum mechanics, I did it in the level of Resnick and Eisberg and Griffiths... Now I want to proceed further in the summer and start with Heisenberg Matrix Mechanics as well... I want recommendation on how to start... I'm thinking of starting with Merzbacher and R.Shankar...
 
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I really suggest the book by Ballentine, supplemented by Shankar :)
 
I second Ballentine, and recommend that you read Isham on the side, or before you start with Ballentine. (Isham is much easier, but should help your understanding a lot).

"Matrix mechanics" is an obsolete term. The theory that these books will teach you is based on the Hilbert space approach to quantum theory that von Neumann came up with in the late 1920s, or rather Dirac's version of it from the early 1930s. (I reserve the right to be completely wrong about the history of QM :smile:)
 
I recommend the courses by Prof.V.Balakrishnan in Quantum Mechanics on youtube also. He is really good at explaining Hilbert Space even if you don't have much background in linear algebra.
 

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