A quantum quasiharmonic 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 positiondependent mass of the form m(x) = 1/(1 − κx²), with a κdependent nonpolynomial 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:
 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., Email: mfran@unizar.es. A quantum quasiharmonic nonlinear oscillator with an isotonic term. United States: N. p., 2014.
Web. doi:10.1063/1.4892084.
Rañada, Manuel F., Email: mfran@unizar.es. A quantum quasiharmonic nonlinear oscillator with an isotonic term. United States. doi:10.1063/1.4892084.
Rañada, Manuel F., Email: mfran@unizar.es. Fri .
"A quantum quasiharmonic nonlinear oscillator with an isotonic term". United States.
doi:10.1063/1.4892084.
@article{osti_22306084,
title = {A quantum quasiharmonic nonlinear oscillator with an isotonic term},
author = {Rañada, Manuel F., Email: 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 positiondependent mass of the form m(x) = 1/(1 − κx²), with a κdependent nonpolynomial 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}
}

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