Rational solutions for the Riccati-Schrödinger equations associated to translationally shape invariant potentials
arXiv:0910.4810 · doi:10.1016/j.aop.2010.03.008
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.
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