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.

Bijan Kumar Bagchi

Physics

(SoNS) School of Natural Sciences

Syed Mohammad Kamil

Tummuru T.R.

Semorádová I.

Znojil M.

Fulltext

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Shiv Nadar University

Journal of Physics: Conference Series

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.

Generalized Uncertainty Principle and Momentum-Dependent Effective Mass Schrödinger Equation

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.

Modern Physics Letters A

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

General Relativity and Gravitation

Resolving the issue of branched Hamiltonian in modified Lanczos–Lovelock gravity

One of the less well-understood ambiguities of quantization is emphasized to result from the presence of higher-order time derivatives in the Lagrangians resulting in multiple-valued Hamiltonians. We explore certain classes of branched Hamiltonians in the context of nonlinear autonomous differential equation of Liénard type. Two eligible elementary nonlinear models that emerge are shown to admit a feasible quantization along these lines. © 2015 World Scientific Publishing Company.