Klein-Gordon Oscillator in the Presence of External Fields in a Cosmic Space-Time with a Space-Like Dislocation and Aharonov-Bohm Effect

Abstract

In this paper, we study interactions of a scalar particle with electromagnetic potential in the background space-time generated by a cosmic string with a space-like dislocation. We solve the Klein-Gordon oscillator in the presence of external fields including an internal magnetic flux field and analyze the analogue effect to the Aharonov-Bohm effect for bound states. We extend this analysis subject to a Cornell-type scalar potential and observe the effects on the relativistic energy eigenvalue and eigenfunction.

Effects of Kaluza-Klein Theory and Potential on a Generalized Klein-Gordon Oscillator in the Cosmic String Space-Time

“…By imposing the additional recurrence condition c n+1 = 0 on the relativistic eigenvalue problem, for example n = 1, we have obtained the ground state energy levels and wave-functions by Eqs. (26)- (27). We have discussed a special case corresponds to η L ⟶ 0 and obtained the relativistic energy eigenvalues Eq.…”

“…Aharonov-Bohm effect [19][20][21] is a quantum mechanical phenomena that has been investigated in several branches of physics, such as in, graphene [22], Newtonian theory [23], bound states of massive fermions [24], scattering of dislocated wave-fronts [25], torsion effect on a relativistic position-dependent mass system [26,27], and nonminimal Lorentz-violating coupling [28]. In addition, Aharonov-Bohm effect has been investigated in the context of Kaluza-Klein theory by several authors [18,[29][30][31][32][33][34], and the geometric quantum phase in graphene [35].…”

“…(25) into the Eqs. (26)- (27), it is possible to obtain the allowed values of the relativistic energy for the radial mode n = 1 of a position dependent mass system. We can see that the lowest energy state defined by the real solution of the algebraic equation given in Eq.…”

Linear confinement of generalized KG-oscillator with a uniform magnetic field in Kaluza–Klein theory and Aharonov–Bohm effect

“…The relativistic quantum dynamics of spin-0 scalar particle with a scalar potential S ( r ) by modifying the mass term in the form as done in Refs. 27 , 28 , 48 in five-dimensional case is described by 26 , 31 – 33 : where , with is the determinant of metric tensor with its inverse for the line element ( 2 ) and m is rest mass of the particle.…”

“…( 16 ) into the Eq. ( 14 ), we obtain where Equation ( 17 ) is the biconfluent Heun’s differential equation 27 , 28 , 48 , 60 , 73 , 74 and is the Heun polynomials.…”