Branched Hamiltonians for a Class of Velocity Dependent Potentials

Abstract

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 quantization. Within this framework, we pick up a model that samples the latter ambiguities and simultaneously turns out to be amenable to a transparent analytic and perturbative treatment.

Generalized Uncertainty principle and momentum-dependent effective mass Schrodinger equation

“…The interest in such systems stem essentially from the physical problems underlying compositionally graded crystals [28], quantum dots [29], liquid crystals [30] etc. Likewise, a MDM scenario has also found relevance in certain quantum mechanical problems such as in the quantization of a paritysymmetric Liénard type nonlinear oscillator [31] and also in classical problems possessing quantum analogs, for example, in branched Hamiltonian systems [32,33].…”