skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: A quantum quasi-harmonic nonlinear oscillator with an isotonic term

Abstract

The properties of a nonlinear oscillator with an additional term k{sub g}/x², characterizing the isotonic oscillator, are studied. The nonlinearity affects to both the kinetic term and the potential and combines two nonlinearities associated to two parameters, κ and k{sub g}, in such a way that for κ = 0 all the characteristics of the standard isotonic system are recovered. The first part is devoted to the classical system and the second part to the quantum system. This is a problem of quantization of a system with position-dependent mass of the form m(x) = 1/(1 − κx²), with a κ-dependent non-polynomial rational potential and with an additional isotonic term. The Schrödinger equation is exactly solved and the (κ, k{sub g})-dependent wave functions and bound state energies are explicitly obtained for both κ < 0 and κ > 0.

Authors:
 [1]
  1. Dep. de Física Teórica and IUMA, Universidad de Zaragoza, 50009 Zaragoza (Spain)
Publication Date:
OSTI Identifier:
22306084
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 55; Journal Issue: 8; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BOUND STATE; EXACT SOLUTIONS; NONLINEAR PROBLEMS; OSCILLATORS; POTENTIALS; QUANTIZATION; SCHROEDINGER EQUATION; WAVE FUNCTIONS

Citation Formats

Rañada, Manuel F., E-mail: mfran@unizar.es. A quantum quasi-harmonic nonlinear oscillator with an isotonic term. United States: N. p., 2014. Web. doi:10.1063/1.4892084.
Rañada, Manuel F., E-mail: mfran@unizar.es. A quantum quasi-harmonic nonlinear oscillator with an isotonic term. United States. doi:10.1063/1.4892084.
Rañada, Manuel F., E-mail: mfran@unizar.es. Fri . "A quantum quasi-harmonic nonlinear oscillator with an isotonic term". United States. doi:10.1063/1.4892084.
@article{osti_22306084,
title = {A quantum quasi-harmonic nonlinear oscillator with an isotonic term},
author = {Rañada, Manuel F., E-mail: mfran@unizar.es},
abstractNote = {The properties of a nonlinear oscillator with an additional term k{sub g}/x², characterizing the isotonic oscillator, are studied. The nonlinearity affects to both the kinetic term and the potential and combines two nonlinearities associated to two parameters, κ and k{sub g}, in such a way that for κ = 0 all the characteristics of the standard isotonic system are recovered. The first part is devoted to the classical system and the second part to the quantum system. This is a problem of quantization of a system with position-dependent mass of the form m(x) = 1/(1 − κx²), with a κ-dependent non-polynomial rational potential and with an additional isotonic term. The Schrödinger equation is exactly solved and the (κ, k{sub g})-dependent wave functions and bound state energies are explicitly obtained for both κ < 0 and κ > 0.},
doi = {10.1063/1.4892084},
journal = {Journal of Mathematical Physics},
number = 8,
volume = 55,
place = {United States},
year = {Fri Aug 01 00:00:00 EDT 2014},
month = {Fri Aug 01 00:00:00 EDT 2014}
}