The generalized quantum isotonic oscillator

Abstract

Recently, it has been proved that a nonlinear quantum oscillator, generalization of the isotonic one, is exactly solvable for certain values of its parameters. Here we show that the Schroedinger equation for such an oscillator can be transformed into a confluent Heun equation. We give a very simple and efficient algorithm to solve it numerically, no matter what the values of the parameters are. Algebraic quasi-polynomial solutions, for particular values of the parameters, are found.