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.

Bijan Kumar Bagchi

Physics

(SoNS) School of Natural Sciences

Ghosh R.

Goswami P.

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Shiv Nadar University

Journal of Physics: Conference Series

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

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

The European Physical Journal Plus

Ladder operators for the BenDaniel-Duke Hamiltonians and their SUSY partners

Position-dependent mass momentum operator and minimal coupling: point canonical transformation and isospectrality

Journal of Applied Mathematics and Physics

A New Class of Exactly Solvable Models within the Schr&amp;#246;dinger Equation with Position Dependent Mass

Generalized Uncertainty Principle and Momentum-Dependent Effective Mass Schrödinger Equation