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Zbl 0927.34065
Cariñena, J.F.; Marmo, G.; Perelomov, A.M.; Rañada, M.F.
Related operators and exact solutions of Schrödinger equations. (English)
[J] Int. J. Mod. Phys. A 13, No.28, 4913-4029 (1998). ISSN 0217-751X

Summary: The authors consider the Schrödinger equation just as a differential equation, disregarding the physical interpretation associated with solutions. By introducing the notion of $A$-related equations, $A$ being a differential operator, they associate with it a Riccati equation and study the solutions when the potential is a meromorphic function.

MSC 2000:: *34L40 Particular ordinary differential operators
81Q05 Closed and approximate solutions to quantum-mechanical equations
35Q51 Solitons
34M05 Entire and meromorphic solutions
34M55 Painlevé and other special equations

Keywords: Schrödinger equation; Riccati equation; solutions

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