Rational solutions for the Riccati-Schrödinger equations associated to translationally shape invariant potentialsReport as inadecuate




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1 FCN - Fédération de Chimie de Nancy

Abstract : 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 terminating continued fractions in an appropriate variable. We give explicit formulas for all the eigenstates, their specific form depending on the Barclay-Maxwell class to which the considered potential belongs.

keyword : supersymmetric quantum mechanics shape invariant potentials solvable models Riccati equation





Author: Yves Grandati - Alain Bérard -

Source: https://hal.archives-ouvertes.fr/



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