Dirac equation in the curved spacetime and generalized uncertainty principle: A fundamental quantum mechanical approach with energy-dependent potentials

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YEŞİLTAŞ Ö.

EUROPEAN PHYSICAL JOURNAL PLUS, vol.134, no.7, 2019 (SCI-Expanded)

• Publication Type: Article / Article
• Volume: 134 Issue: 7
• Publication Date: 2019
• Doi Number: 10.1140/epjp/i2019-12694-x
• Journal Name: EUROPEAN PHYSICAL JOURNAL PLUS
• Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
• Gazi University Affiliated: Yes

Abstract

In this work, we have obtained the solutions of the (1 + 1)-dimensional Dirac equation on a gravitational background within the generalized uncertainty principle. We have shown that how minimal length parameters effect the Dirac particle in a spacetime described by conformally flat metric. Also, supersymmetric quantum mechanics is used both to factorize the Dirac Hamiltonians and obtain new metric functions. Finally, it is observed that the energy-dependent potentials may be extended to the energy-dependent metric functions.