Klein–Gordon field in spinning cosmic-string space-time with the Cornell potential

Abstract

We study the relativistic quantum dynamics of a Klein–Gordon scalar field subject to a Cornell potential in spinning cosmic-string space-time, in order to better understand the effects of gravitational fields produced by topological defects on the scalar field. We solve the Klein–Gordon equation in the presence of scalar and vector interactions by utilizing the Nikiforov–Uvarov formalism and two ansätze, one of which leads to a biconfluent Heun differential equation. We obtain the wave-functions and the energy levels of the relativistic field in that space-time. We discuss the effect of various physical parameters and quantum numbers on the wave-functions.

The Dirac equation in a class of topologically trivial flat Gödel-type space-time backgrounds

“…The obtained eigenvalues of energy in these different classes of Gödel-type space-times are found different and the results are enough significant [71,76]. Other works are the quantum dynamics of Klein-Gordon scalar field subject to Cornell potential [82], survey on the Klein-Gordon equation in a class of Gödel-type space-times [83], the Dirac-Weyl equation in graphene under a magnetic field [84], effects of cosmic string framework on thermodynamical properties of anharmonic oscillator [85], study of bosons for three special limits of Gödel-type space-times [86], the Klein-Gordon oscillator in the presence of Cornell potential in the cosmic string space-time [87], the covariant Duffin-Kemmer-Petiau (DKP) equation in the cosmic-string space-time with interaction of a DKP field with the gravitational field produced by topological defects investigated in [88], the Klein-Gordon field in spinning cosmic string space-time with the Cornell potential [89], the relativistic spin-zero bosons in a Som-Raychaudhuri space-time investigated in [90], investigation of the Dirac equation using the conformable fractional derivative [91], effect of the Wigner-Dunkl algebra on the Dirac equation and Dirac harmonic oscillator investigated in [92], investigation of the relativistic dynamics of a Dirac field in the Som-Raychaudhuri space-time, which is described by Gödel-type metric and a stationary cylindrical symmetric solution of Einstein's field equations for a charged dust distribution in rigid rotation [93], investigation of relativistic free bosons in the Gödel-type spacetimes [94], investigation of relativistic quantum dynamics of a DKP oscillator field subject to a linear interaction in cosmic string space-time to understand the effects of gravitational fields produced by topological defects on the scalar field [95], the behaviour of relativistic spin-zero bosons in the space-time generated by a spinning cosmic string investigated in [96], relativistic spin-0 system in the presence of a Gödel-type background space-time investigated in [97], study of the Duffin-Kemmer-Petiau (DKP) equation for spin-zero bosons in the space-time generated by a cosmic string subject to a linear interaction of a DKP field with gravitational fields produced by topological defects investigated in [98], the information-theoretic measures of (1 + 1)dimensional Dirac equation in both position and momentum spaces are investigated for the trigonometric Rosen-Morse and the Morse potentials investigated in [99], analytical bound and scattering state solutions of Dirac equation for the modified deformed Hylleraas potential with a Yukawat...…”

Quantum Influence of Topological Defects on a Relativistic Scalar Particle with Cornell-Type Potential in Cosmic String Space-Time with a Spacelike Dislocation

“…One can obtain the individual energy eigenvalues one by one, that is, E 1 , E 2 , E 3 by imposing the additional recurrence condition c n+1 = 0 on the eigenvalue. The solution with Heun's Equation makes it possible to obtain the eigenvalues one by one as done in [3,5,7,12,19,50,51,52,53,54,57,59,71,74,85,86,92,93] but not explicitly in the general form by all eigenvalues n. With the aim of obtaining the energy levels of the stationary states, let us discuss a particular case of n = 1. This means that we want to construct a polynomial of first degree to H(x).…”

“…, we can see that the power series expansion H(x) becomes a polynomial of degree n by imposing the following two conditions[3,5,7,12,19,50,51,52,53,54,57,59,71,74,85,86,92,93] Θ = 2 n, (n = 1, 2, ....)…”

Effects of Lorentz Symmetry Breaking and scalar Potential on Relativistic Quantum Oscillator

“…The relativistic quantum dynamics of scalar particle by solving the KGoscillator in various space-times background has been investigated by many authors [1,2,3,4,5,6,7,8,9,10,11]. The Klein-Gordon oscillator [12] 1 faizuddinahmed15@gmail.com ; faiz4U.enter@rediffmail.com was inspired by the Dirac oscillator [13] applied for spin- 1 2 particle.…”