skip to main content

SciTech ConnectSciTech Connect

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

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)
Publisher:
American Institute of Physics (AIP)
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