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Related operators and exact solutions of Schrödinger equations. (English) Zbl 0927.34065
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:
34L40Particular ordinary differential operators
81Q05Closed and approximate solutions to quantum-mechanical equations
35Q51Soliton-like equations
34M05Entire and meromorphic solutions (ODE)
34M55Painlevé and other special equations; classification, hierarchies