Bound state solutions of D-dimensional schrödinger equation with exponential-type potentials

• Published in: International journal of quantum chemistry Vol. 115; no. 3; pp. 158 - 164
• Main Authors: Peña, José Juan, García-Martínez, Jesús, García-Ravelo, Jesus, Morales, Jesus
• Format: Journal Article
• Language: English; French; German
• Published: Hoboken Blackwell Publishing Ltd 05.02.2015; Wiley Subscription Services, Inc
• Subjects: Bound state solutions; Canonical transformation; Chemistry; Exponential-type potentials; Physical chemistry; Quantum physics; Schrödinger equation
• ISSN: 0020-7608; 1097-461X
• DOI: 10.1002/qua.24803

In this article, using an exactly‐solvable multiparameter exponential‐type potential we propose a unified treatment of the analytical bound—state solutions of the Schrödinger equation for exponential‐type potentials in D‐dimensions. Our proposal accepts different approximations to the centrifugal term; however, its usefulness is exemplified in the frame of the Green and Aldrich approach. This fact enables us to compare our results with specific potentials found in the literature and that are obtained here as particular cases of our proposal. That is, instead of solving a specific exponential‐type potential, by resorting each time to a specialized method, the energy spectra and wavefunctions are derived straightforward from the proposed approach. Furthermore, our proposal can be used as an alternative way in the search of solutions to new exponential‐type potentials besides that one can study different approximations to the term 1/r2. © 2014 Wiley Periodicals, Inc. The quantum‐chemical structure of a molecule is summarized in its potential energy curves where the minimum determines the bond lengths and the second derivative determines the force constants that lead to vibrational and rotational levels. This perspective discusses the solution of a class of multiparameter exponential‐type potential where a suitable selection of the parameters gives rise to a specific potential. The proposal provides the energy spectra and wave‐functions.