I'm a mathematics undergraduate student and I think of studying QM this summer. I've found two online courses given by professor Fredric Schuller QM (link). I look for a good text that I can use to accompany those lectures. I prefer those lectures since they are rigorous unlike most courses I've found on Youtube that are not rigorous enough for my tastes.

Which texts do you recommend? What about Principles of Quantum Mechanics by Shankar? does it go along with the QM course? if not, any other recommendations?

I've suggested the two books since when I skimmed through them, they seemed to be more rigorous than many other texts I skimmed through. Note also that It will be my first course to QM and GR.

Here are the titles of lectures of QM course (every lecture is about 110 minutes):

  1. Axioms of Quantum Mechanics

  2. Banach Spaces

  3. Separable Hilbert spaces

  4. Projectors,bars and kets

  5. Measure Theory

  6. Integration of measurable functions

  7. Self adjoint and essentially self-adjoint operators

  8. Spectra and perturbation theory

  9. Case study: momentum operator

  10. Inverse Spectral Theorem

  11. Spectral Theorem

  12. Stone's theorem & construction of observables

  13. Spin

  14. Composite systems

  15. Total spin of composite system -

  16. Quantum Harmonic Oscillator I

  17. Quantum Harmonic Oscillator II

  18. The Fourier Operator

  19. The Schrodinger Operator

  20. Periodic potentials I

  21. Periodic potentials II

  • 2
    $\begingroup$ This needs to be separated into one post about QM and a separate one about GR. However, note that both of those would probably be duplicates. $\endgroup$
    – DanielSank
    Jun 3 '16 at 16:36
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    $\begingroup$ Second, please do not expect readers to click on links and read about extra information. If there's something in the links that's important to your question, then include that information directly in the question. If you want to know what book goes with a particular curriculum, include that curriculum in your post. $\endgroup$
    – DanielSank
    Jun 3 '16 at 16:37
  • $\begingroup$ James Binney at Oxford has an excellent online QM course, and he has the full notes/ transcript of it for free on his website. $\endgroup$
    – user108787
    Jun 3 '16 at 16:50
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    $\begingroup$ @DanielSank Tbh I think it was quite fine to have both in the one post, since both courses were given by Frederick Schuller. So what books complement his style/rigour $\endgroup$
    – snulty
    Jun 4 '16 at 11:46
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    $\begingroup$ @Astring ah good, hopefully you'll get the answer to the original question you asked so! I'm tempted to add some suggestions myself. $\endgroup$
    – snulty
    Aug 2 '16 at 22:13

Best books about basic QM which I used are: Dirac, Messiah and Sakurai. None of this is completely rigorous but I don't think it's possible to find a book which is completely rigorous mathemathically and also explains basic physical content of the theory. For GR situation is much better in this regard, because classical field theory is much better understood. I suggest book by Wald. It is one of the best physics textbooks which I ever used.

Word of caution: there is no way that you understand well GR and QM in one summer.

  • $\begingroup$ @A String And from my experience, you NEED to do all the problems to really make you think about it, which takes more time. Best of luck with it. $\endgroup$
    – user108787
    Jun 3 '16 at 17:02

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