Non-Archimedean quantum mechanics via quantum groups

Authors

Wilson A. Zuniga-Galindo, The University of Texas Rio Grande Valley

Document Type

Article

Publication Date

12-2022

Abstract

We present a new non-Archimedean realization of the Fock representation of the q-oscillator algebras where the creation and annihilation operators act on complex-valued functions, which are defined on a non-Archimedean local field of arbitrary characteristic, for instance, the field of p-adic numbers. This new realization implies that many quantum models constructed using q-oscillator algebras are non-Archimedean models, in particular, p-adic quantum models. In this framework, we select a q-deformation of the Heisenberg uncertainty relation and construct the corresponding q-deformed Schrödinger equations. In this way we construct a p-adic quantum mechanics which is a p-deformed quantum mechanics. We also solve the time-independent Schrödinger equations for the free particle, and a particle in a non-Archimedean box. In the last case, we show the existence of a discrete sequence of energy levels. We determine the eigenvalues of Schrödinger operator for a general radial potential. By choosing the potential in a suitable form we recover the energy levels of the q-hydrogen atom.

Comments

© 2022 The Author(s). Published by Elsevier B.V.

Recommended Citation

Zuniga-Galindo, Wilson A. "Non-Archimedean quantum mechanics via quantum groups." Nuclear Physics B 985 (2022): 116021. https://doi.org/10.1016/j.nuclphysb.2022.116021

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Publication Title

Nuclear Physics B

DOI

10.1016/j.nuclphysb.2022.116021