Rational solutions for the Riccati-Schrödinger equations associated to translationally shape invariant potentials

Details Rational solutions for the Riccati-Schrödinger equations associated to translationally shape invariant potentials Rational solutions for the Riccati-Schrödinger equations associated to translationally shape invariant potentials

2009-10-26

arxiv.org/abs/0910.4810v3

Physics

Mathematical Physics

Scientific paper

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.

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