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

Journal Article · Tue Jun 15 00:00:00 EDT 2010 · Annals of Physics (New York)

DOI:https://doi.org/10.1016/j.aop.2010.03.008· OSTI ID:21452979

Grandati, Y ^[1]; Berard, A ^[1]

---

1. Institut de Physique, ICPMB, IF CNRS 2843, Universite Paul Verlaine, 1 Bd Arago, 57078 Metz, Cedex 3 (France)

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.

• OSTI ID: 21452979
• Journal Information: Annals of Physics (New York), Vol. 325, Issue 6; Other Information: DOI: 10.1016/j.aop.2010.03.008; PII: S0003-4916(10)00060-6; Copyright (c) 2010 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; ISSN 0003-4916
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CONTINUED FRACTIONS
EIGENFUNCTIONS
MATHEMATICAL SOLUTIONS
POTENTIALS
QUANTUM MECHANICS
SCHROEDINGER EQUATION
SUPERSYMMETRY
DIFFERENTIAL EQUATIONS
EQUATIONS
FUNCTIONS
MECHANICS
PARTIAL DIFFERENTIAL EQUATIONS
SYMMETRY
WAVE EQUATIONS