doi:10.1063/1.4892084]engRañada, M. F.A quantum quasi-harmonic nonlinear oscillator with an isotonic termART-2014-108591The properties of a nonlinear oscillator with an additional term kg/x2, character- izing the isotonic oscillator, are studied. The nonlinearity affects to both the kinetic term and the potential and combines two nonlinearities associated to two parameters, ¿ and kg, in such a way that for ¿ = 0 all the characteristics of of the standard isotonic system are recovered. The first part is devoted to the classical system and the sec- ond 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 - ¿x2), with a ¿-dependent non- polynomial rational potential and with an additional isotonic term. The Schr ¨odinger equation is exactly solved and the (¿,kg)-dependent wave functions and bound state energies are explicitly obtained for both ¿ < 0 and ¿ > 0.2014http://zaguan.unizar.es/record/7726510.1063/1.4892084]http://zaguan.unizar.es/record/77265oai:zaguan.unizar.es:77265info:eu-repo/grantAgreement/ES/DGA/E24-1info:eu-repo/grantAgreement/ES/MICINN/MTM2012-33575JOURNAL OF MATHEMATICAL PHYSICS 55, 8 (2014), 082108 (12 pp.)by-nc-ndhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/info:eu-repo/semantics/openAccess