Abstract
We constructdeformed annihilation and creation, operators of the harmonic oscillator context in terms of the parity operator and realize, in that way the superalgebrasqm(2) of supersymmetric quantum mechanics. Moreover, this specific example is related to the physical application known as the Calogero problem. The reducibility, of supersymmetric quantum mechanics is then established for arbitraryodd superpotentials, but not for even ones. We also get (minimal) dynamical algebras in both cases, shedding new light on such physical quantities as the Runge-Lenz vector.
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Beckers, J., Debergh, N. & Nikitin, A.G. Reducibility of supersymmetric quantum mechanics. Int J Theor Phys 36, 1991–2003 (1997). https://doi.org/10.1007/BF02435955
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DOI: https://doi.org/10.1007/BF02435955