On Quantized Lienard Oscillator and Momentum Dependent Mass

TL;DR

This paper analyzes the nonlinear Lienard oscillator, revealing its bi-Hamiltonian nature depending on parameters, and provides exact solutions for related Hamiltonians involving momentum-dependent mass and isotonic characteristics.

Contribution

It uncovers the bi-Hamiltonian structure of the Lienard oscillator and derives explicit solutions for Hamiltonians with momentum-dependent mass.

Findings

Identification of bi-Hamiltonian structure based on coupling parameters

Derivation of complete solutions using confluent hypergeometric functions

Connection between the Hamiltonian and isotonic oscillator features

Abstract

We examine the analytical structure of the nonlinear Lienard oscillator and show that it is a bi-Hamiltonian system depending upon the choice of the coupling parameters. While one has been recently studied in the context of a quantized momentum- dependent mass system, the other Hamiltonian also reflects a similar feature in the mass function and also depicts an isotonic character. We solve for such a Hamiltonian and give the complete solution in terms of a confluent hypergeometric function.