I am looking to learn about how one can use group theory methods to obtain the spectrum of a hydrogenic atom algebraically. I have found many such resources online, such as this paper: http://web.mit.edu/lululiu/Public/8.06/paper.pdf

However, most assume more working knowledge of group theory/Lie algebra than I have. Could anyone provide me with a reference to a textbook or paper/article which derives this result without assuming too much background knowledge? I'm looking for something pedagogic.

  • 2
    $\begingroup$ You might want to look at the pages 235 up to 244 of Kurt Gottfried's book on QM (2nd edition, 2003). $\endgroup$
    – M_kaj
    Commented Mar 12, 2021 at 10:42
  • $\begingroup$ This post has an excellent answer discussing the Lenz vector: physics.stackexchange.com/questions/18088/… $\endgroup$
    – my2cts
    Commented Mar 12, 2021 at 11:44

1 Answer 1


If you want to learn about both Lie groups and how to solve the Hydrogen atom using those, I would recommend "Lie groups, physics, and geometry" by Gilmore.

It is well written, with physics and engineering students in mind, with lots of examples on simple cases. The first six or seven chapters are very nice (then it can go too deep into classification to my taste).

Chapter 14 is all about solving the Hydrogen atom using what was developed in the previous chapters.

  • $\begingroup$ For anyone else who might be interested, I found that he actually hosts the relevant chapters for free on his website: physics.drexel.edu/~bob/LieGroups.html $\endgroup$
    – dsfkgjn
    Commented Mar 12, 2021 at 14:15
  • $\begingroup$ Indeed, not much is missing! $\endgroup$
    – Adam
    Commented Mar 12, 2021 at 19:02

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