A quantum quasi-harmonic nonlinear oscillator with an isotonic term

作者：Ranada Manuel F^*

来源：Journal of Mathematical Physics, 2014, 55(8): 082108.

DOI：10.1063/1.4892084

The properties of a nonlinear oscillator with an additional term k(g)/x(2), 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, kappa and k(g), in such a way that for kappa = 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 - kappa x(2)), with a kappa-dependent non-polynomial rational potential and with an additional isotonic term. The Schrodinger equation is exactly solved and the (kappa, k(g))-dependent wave functions and bound state energies are explicitly obtained for both kappa %26lt; 0 and kappa %26gt; 0.

• 出版日期2014-8