We propose a new form of Lagrangian that shows branching for the associated Hamiltonian and has relevance to the quadratic type and mixed linear-quadratic Liénard-type nonlinear dynamical equations on adjusting the underlying parameters. Non-uniqueness of the Lagrangian is pointed out and a particular one when Fourier transform is demonstrated to depict a momentum-dependent quantum-like mass system when expanded binomially. © 2019 World Scientific Publishing Company.

Bijan Kumar Bagchi

Physics

(SoNS) School of Natural Sciences

Ghosh D.

Modak S.

Panigrahi P.K.

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Shiv Nadar University

Nonstandard Lagrangians and branching: The case of some nonlinear Liénard systems

Modern Physics Letters A

We show in this paper that the basic representations of position and momentum in a quantum mechanical system, that are guided by a generalized uncertainty principle and lead to a corresponding one-parameter eigenvalue problem, can be interpreted in terms of an extended Schrödinger equation embodying momentum-dependent mass. Some simple consequences are pointed out. © Published under licence by IOP Publishing Ltd.

Fulltext

Journal of Physics: Conference Series

Generalized Uncertainty Principle and Momentum-Dependent Effective Mass Schrödinger Equation

Hamiltonians that are multivalued functions of momenta are of topical interest since they correspond to the Lagrangians containing higher-degree time derivatives. Incidentally, such classes of branched Hamiltonians lead to certain not too well understood ambiguities in the procedure of the quantization. Within this framework we pick up a model which samples the latter ambiguities and which, simultaneously, turns out to be amenable to a transparent analytic and perturbative treatment. © Published under licence by IOP Publishing Ltd.

Branched Hamiltonians for a Class of Velocity Dependent Potentials

Journal of Engineering Mathematics

Two-dimensional isochronous nonstandard Hamiltonian systems

Pramana

Isochronous Liénard-type nonlinear oscillators of arbitrary dimensions

Physica Scripta

One-parameter supersymmetric Hamiltonians in momentum space

We examine the analytical structure of the nonlinear Liénard 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. © 2015 AIP Publishing LLC.

Journal of Mathematical Physics