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arXiv · 1803.01020

Bohmian mechanics and Fisher information for $q$-deformed Schr\"odinger equation

Bruno G. da Costa·Ignacio S. Gomez
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Abstract

We discuss the Bohmian mechanics by means of the deformed Schr\"odinger equation for position dependent mass, in the context of a $q$-algebra inspired by nonextensive statistics. A deduction of the Bohmian quantum formalism is performed by means of a deformed Fisher information functional, from which a deformed Cram\'er-Rao bound is derived. Lagrangian and Hamiltonian formulations, inherited by the $q$-algebra, are also developed. Then, we illustrate the results with a particle confined in an infinite square potential well. The preservation of the deformed Cram\'er-Rao bound for the stationary states shows the role played by the $q$-algebraic structure.

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Bruno G. da Costa, Ignacio S. Gomez. 2018-03-02. Bohmian mechanics and Fisher information for $q$-deformed Schr\"odinger equation. https://arxiv.org/abs/1803.01020

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