Abstract
We discuss the Bohmian mechanics using a deformed Schrödinger equation for position-dependent mass systems, in the context of a q-algebra inspired by the nonextensive statistical mechanics. We obtain the Bohmian quantum formalism by means of a deformed version of the Fisher information functional, from which a deformed Cramér–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 Cramér–Rao bound for eigenstates shows the role played by the q-algebraic structure.
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