Shape Invariant potentials depending on n parameters transformed by translation

Details Shape Invariant potentials depending on n parameters transformed by translation Shape Invariant potentials depending on n parameters transformed by translation

2000-03-29

arxiv.org/abs/hep-th/0003266v1

J.Phys.A33:3467-3481,2000

Physics

High Energy Physics

High Energy Physics - Theory

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

Scientific paper

10.1088/0305-4470/33/17/305

Shape Invariant potentials in the sense of [Gendenshte\"{\i}n L.\'E., 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.

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