Solvable rational extensions of the isotonic oscillator

Physics – Mathematical Physics

Scientific paper

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Scientific paper

10.1016/j.aop.2011.03.001

Combining recent results on rational solutions of the Riccati-Schr\"odinger equations for shape invariant potentials to the finite difference B\"acklund algorithm and specific symmetries of the isotonic potential, we show that it is possible to generate the three infinite sets (L1, L2 and L3 families) of regular rational solvable extensions of this potential in a very direct and transparent way.

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