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math-ph2009★ 27 cited
Rational solutions for the Riccati-Schrödinger equations associated to translationally shape invariant potentials
Yves Grandati, Alain Bérard
We develop a new approach to build the eigenfunctions of a translationally shape-invariant potential. For this we show that their logarithmic derivatives can be expressed as termin…
math-ph2006★ 21 cited
Inverse problem and Bertrand's theorem
Yves Grandati, Alain Bérard, Ferhat Menas
The Bertrand's theorem can be formulated as the solution of an inverse problem for a classical unidimensional motion. We show that the solutions of these problems, if restricted to…