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 $n=0$).

arXiv comment24 pages, 5 figures

References in corpus (35)

• Exact Mapping of the 2+1 Dirac Oscillator onto the Jaynes-Cummings Model: Ion-Trap Experimental Proposal
• First experimental realization of the Dirac oscillator
• Minimal Geometric Deformation in a cloud of strings
• Energy spectrum of a 2D Dirac electron in the presence of a constant magnetic field
• Relativistic quantum oscillators in the global monopole spacetime
• Chirality Quantum Phase Transition in the Dirac oscillator
• Dirac quasinormal modes of the Reissner-Nordström de Sitter black hole
• Exact solution of the two-dimensional Dirac oscillator
• Noninertial effects on the Dirac oscillator in a topological defect spacetime
• Relativistic quantum mechanics of a Dirac oscillator
• Tideless Traversable Wormholes surrounded by cloud of strings in $f(R)$ gravity
• Relativistic R matrix and continuum shell model
• Kerr black hole surrounded by a cloud of strings and its weak gravitational lensing in Rastall gravity
• Bound state solutions of the Dirac oscillator in an Aharonov-Bohm-Coulomb system
• Quasinormal mode and spectroscopy of a Schwarzschild black hole surrounded by a cloud of strings in Rastall gravity
• On the Letelier spacetime with quintessence: solution, thermodynamics and Hawking radiation
• Bardeen solution with a cloud of strings
• Hermitian Dirac Hamiltonian in time dependent gravitational field
• Energy spectrum of the ground state of a two dimensional relativistic hydrogen atom in the presence of a constant magnetic field
• The noncommutative quantum Hall effect with anomalous magnetic moment in three different relativistic scenarios
• Pseudospectral computational methods for the time-dependent Dirac equation in static curved spaces
• 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
• Thermodynamics of Quantum Phase Transitions of a Dirac oscillator in a homogenous magnetic field
• Gate-Tunable Graphene Quantum Dot and Dirac Oscillator
• Integrability of Kerr-Newman spacetime with cloud strings, quintessence and electromagnetic field
• Fermionic greybody factors in dilaton black holes
• The Angular Momentum Operator in the Dirac Equation
• Quantum Effects for the Dirac Field in Reissner-Nordstrom-AdS Black Hole Background
• The Dirac oscillator: an alternative basis for nuclear structure calculations
• Stationary Solutions of the Dirac Equation in the Gravitational Field of a Charged Black Hole
• Relativistic and nonrelativistic Landau levels for the noncommutative quantum Hall effect with anomalous magnetic moment in a conical Gödel-type spacetime
• Asymptotic Behavior of Massless Dirac Waves in Schwarzschild geometry
• Dirac fermions in a spinning conical Gödel-type spacetime
• Black Strings and String Clouds Embedded in Anisotropic Quintessence: Solutions for Scalar Particles and Implications