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I want to study SUSY QM. I found some excellent physically motivated articles on Arxiv. Despite, I am especially interested in the mathematical structure behind SUSY QM. Does anybody know whether there is a particularly good reference to start studying SUSY QM from a rigorous mathematical point of view. The reference should cover Spectral analysis and a wide range of all the algebraic properties concerned with the topic.

This post imported from StackExchange Physics at 2014-04-13 14:33 (UCT), posted by SE-user Lipschitz

The original article is still among the best:

But I would suggest to start with this one here

and read Witten in parallel.

For more see the references listed here

If you are just interested in the quantum mechanics of SUSY (rather than its quantum field theory), you should read the comprehensive (though now 20 years old and no longer fully up to date) survey article

F. Cooper, A. Khare, U. Sukhatme, Supersymmetry and quantum mechanics, Physics Reports 251 (1995), 267-385. http://jensen.thphys.uni-heidelberg.de/~maniatis/LectureAdv/SusyQM.pdf

The math is straightforward analysis of ODEs, so no special safeguards are needed.

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