[Math] Resource for learning quantum mechanics from the viewpoint of representation theory

mp.mathematical-physicsquantum mechanicsreference-requestrt.representation-theory

Quantum mechanics is deeply connected with representation theory. Therefore, I'm looking for a textbook or article which presents quantum mechanics in a representation theoretic manner. Could anyone provide me a reference to such a resource? I don't care if it's a math or physics book as long as it makes use of the language of representation theory mathematicians are familiar with.

Best Answer

Here are some references.

  1. Hermann Weyl, The Theory of Groups and Quantum Mechanics, Dover Publications, 1950
  2. George W. Mackey, Induced representations of groups and quantum mechanics, W. A. Benjamin, 1968
  3. M. Gourdin , Unitary Symmetries, John Wiley & Sons, New York, 1968.
  4. A.R. Edmonds, Angular Momentum in Quantum Mechanics, Princeton, 1968
  5. L. C. Biedenharn, James D. Louck, Angular Momentum in Quantum Physics: Theory and Application, Cambridge University Press, 2009
  6. Gianni Cassinelli, The Theory of Symmetry Actions in Quantum Mechanics: With an Application to the Galilei Group, Springer, 2004

I believe 1 and 2 are classics, 3 and 4 probably nearly so. I'm not familiar with 5 nor 6 in detail, but they look interesting - I'm very curious to see comments by other users on any of the above.

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