The Dirac oscillator in the curved spacetime of a cloud of strings

Abstract

In this paper, we determine the relativistic bound-state solutions for the Dirac oscillator (DO) in the curved spacetime of a cloud of strings in $(3+1)$-dimensions, where such solutions are given by the four-component normalized Dirac spinor and by the relativistic energy spectrum. However, unlike in literature, here, we work with the spacetime in two different forms/configurations, that is, both in its original form and in its modified form. To achieve our objective, we work with the curved DO in spherical coordinates, where we use the tetrad formalism. So, by defining a stationary ansatz for the spinor, we obtain two coupled first-order differential equations, and by substituting one equation into the other, we obtain a second-order differential equation. To analytically and exactly solve this differential equation, we use a change of function and of variable. From this, we obtain the well-known Whittaker equation, whose solution is the Whittaker function. Consequently, we obtain the energy spectrum, which is quantized in terms of the radial quantum number $n$ and the angular quantum number $\kappa$, and explicitly depends on the angular frequency $\omega$ (describes the DO), curvature parameter $a$ (describes the cloud of strings), and on the effective rest mass $m_{\text{eff}}$ (describes the rest mass modified by the curvature of spacetime). Besides, we graphically analyze the behavior of the spectrum as a function of $\omega$ and $a$ for three different values of $n$ and $\kappa$, as well as the behavior of the radial probability density for four different values of $\kappa$, $\omega$, and $a$ (with $n=0$).

24 pages, 5 figures

References in corpus (14)

• Exact Mapping of the 2+1 Dirac Oscillator onto the Jaynes-Cummings Model: Ion-Trap Experimental Proposal
• Chirality Quantum Phase Transition in the Dirac oscillator
• Noninertial effects on the Dirac oscillator in a topological defect spacetime
• Tideless Traversable Wormholes surrounded by cloud of strings in $f(R)$ gravity
• Relativistic R matrix and continuum shell model
• Bardeen solution with a cloud of strings
• The noncommutative quantum Hall effect with anomalous magnetic moment in three different relativistic scenarios
• Thermodynamics of a newly constructed black hole coupled with nonlinear electrodynamics and cloud of strings
• Revisiting diagonal tetrads: New Black Hole solutions in $f(T)$ gravity
• Integrability of Kerr-Newman spacetime with cloud strings, quintessence and electromagnetic field
• Quantum Effects for the Dirac Field in Reissner-Nordstrom-AdS Black Hole Background
• Relativistic and nonrelativistic Landau levels for the noncommutative quantum Hall effect with anomalous magnetic moment in a conical Gödel-type spacetime
• Dirac fermions in a spinning conical Gödel-type spacetime
• Black Strings and String Clouds Embedded in Anisotropic Quintessence: Solutions for Scalar Particles and Implications