Shape Invariant potentials depending on n parameters transformed by translation

Abstract

Shape Invariant potentials in the sense of [Gendenshte\"ın L.É., JETP Lett. 38, (1983) 356] which depend on more than two parameters are not know to date. In [Cooper F., Ginocchio J.N. and Khare A., Phys. Rev. {\bf 36 D}, (1987) 2458] was posed the problem of finding a class of Shape Invariant potentials which depend on n parameters transformed by translation, but it was not solved. We analyze the problem using some properties of the Riccati equation and we find the general solution.

19 pages, Latex, iopart.sty, to appear in J. Phys. A: Math. Gen. (2000)

References in corpus (3)

• Riccati equation, Factorization Method and Shape Invariance
• The nonlinear superposition principle and the Wei-Norman method
• Integrability of Riccati equation from a group theoretical viewpoint

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