Branched Hamiltonians for a quadratic type Li\'enard oscillator

TL;DR

This paper investigates the branching behavior of Hamiltonians in quadratic Li'enard oscillators and derives a quantum version with a momentum-dependent mass under specific approximations.

Contribution

It introduces the concept of Hamiltonian branching in quadratic Li'enard oscillators and formulates a quantum model with a momentum-dependent mass.

Findings

Hamiltonian exhibits branching due to double-valuedness.

Quantum counterpart derived with momentum-dependent mass.

Provides insight into the quantum behavior of nonlinear oscillators.

Abstract

We point out that when a quadratic type Li\'enard equation is suitably interpreted shows branching due to the double valuedness of the governing Hamiltonian. Under certain approximation of the guiding coupling constant we derive its quantum counterpart that is guided by a momentum-dependent mass function.