Recursion operators, higher-order symmetries and superintegrability in quantum mechanics |
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| Authors: | M B Sheftel P Tempesta P Winternitz |
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| Institution: | (1) Feza Gürsey Institute, PO Box 6, Cengelkoy, 81220 Istanbul, Turkey;(2) Department of Higher Mathematics, North Western Polytechnical Institute, Millionnaya Str. 5, 191186 St. Petersburg, Russia;(3) Università di Lecce and INFN sez. di Lecce, via per Arnesano, 73100 Lecce, Italy;(4) Centre de Recherches Mathématiques and Dép. de Mathématiques et Statistique, Université de Montréal, C.P. 6128-CV, H3C3J7 Montréal, QC, Canada |
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| Abstract: | A connection between the theory of superintegrable quantum-mechanical systems, which admit a maximal number of integrals of motion, and the standard Lie group theory is established. It is shown that the flows generated by first- and second-order Lie symmetries of the bidimensional Schrödinger equation can be classified and interpreted as quantum-mechanical operators which commute with integrable or superintegrable Hamiltonians. In this way, all known superintegrable potentials in the plane are naturally obtained and slightly more general integrals of motion are found. |
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