Exactly solvable combined potentials and their isospectral partners from SUSY

Autor: J. Morales, J. J. Peña, J. L. López-Bonilla, Mario Romero-Romo
Rok vydání: 2005
Předmět:
Zdroj: International Journal of Quantum Chemistry. 105:731-739
ISSN: 1097-461X
0020-7608
DOI: 10.1002/qua.20687
Popis: In some quantum chemical applications, the potential models are linear combination of single exactly solvable potentials. This is the case, for example, of the equivalent of the Stark effect for a charged harmonic oscillator (HO) in a constant electric field or an HO in an external dipole field. The same occurs with some molecular systems where the determination of the vibrational spectra remains essentially as a numerical task; the Morse and Hulthen potentials are convenient models for the potential energy of a diatomic molecule. In this work, the supersymmetry (SUSY) and shape invariance methods used to determine exactly solvable potentials are extended to obtain, in a closed form, the eigenvalues of exactly solvable combined potentials, as well as their isospectral or generalized partner potentials. Essentially, the proposal is based on the existence of the Witten superpotential [W(x)] associated with single exactly solvable potentials to find the Witten superpotential for the combined potential under study. For instance, the assumption of two W(x) allows to obtain an exactly solvable combined potential which is given by a linear combination between the former potentials plus a term resulting from the product of the two single W(x). The corresponding generalized partner potentials comes from the involved Riccati equation when the resulting Witten superpotential for the combined potential is taken as a specific solution. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005
Databáze: OpenAIRE
Externí odkaz:
Nepřihlášeným uživatelům se plný text nezobrazuje