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arXiv · 2204.00687

Self-adjoint extensions for a $p^{4}$-corrected Hamiltonian of a particle on a finite interval

B. B. Dilem·J. C. Fabris·J. A. Nogueira
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Abstract

In the present paper we deal with the issue of finding the self-adjoint extensions of a $p^4$-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 $U(4)$ parametrization that leads to the self-adjoint extensions. Once the parametrization is known, we can choose appropriate $U(4)$ 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.

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B. B. Dilem, J. C. Fabris, J. A. Nogueira. 2022-04-01. Self-adjoint extensions for a $p^{4}$-corrected Hamiltonian of a particle on a finite interval. https://doi.org/10.1016/j.aop.2022.168994

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