Self-adjoint extensions for a $p^{4}$-corrected Hamiltonian of a particle on a finite interval
Abstract
In the present paper we deal with the issue of finding the self-adjoint extensions of a -corrected Hamiltonian. The importance of this subject lies on the application of the concepts of quantum mechanics to the minimal-length scale scenario which describes an effective theory of quantum gravity. We work in a finite one dimensional interval and we give the explicit parametrization that leads to the self-adjoint extensions. Once the parametrization is known, we can choose appropriate matrices to model physical problems. As examples, we discuss the infinite square-well, periodic conditions, anti-periodic conditions and periodic conditions up to a prescribed phase. We hope that the parametrization we found will contribute to model other interesting physical situations in further works.
Keywords
Cite
@article{arxiv.2204.00687,
title = {Self-adjoint extensions for a $p^{4}$-corrected Hamiltonian of a particle on a finite interval},
author = {B. B. Dilem and J. C. Fabris and J. A. Nogueira},
journal= {arXiv preprint arXiv:2204.00687},
year = {2022}
}