Tensor coupling and relativistic spin and pseudospin symmetries of the Pöschl–Teller-like potential

Abstract

In this research, we have been obtained the Dirac equation for second Pöschl-Teller-like potential including a Coulomb-like tensor interaction with arbitrary spin-orbit coupling quantum number j. Under the condition of spin and pseudospin (p-spin) symmetries, we use the basic concept of the supersymmetric shape invariance formulism in quantum mechanics and the function analysis method to obtain energy eigenvalues and corresponding two-component spinors of the Dirac particle. We have also shown that tensor interaction removes degeneracies between spin and p-spin doublets. Some numerical results are also given.

Relativistic Killingbeck energy states under external magnetic fields

“…Also, in recent years, the exact analytical solutions of the Dirac equation have been extensively obtained, by using various methods in the presence of the spin and p-spin symmetries (see, for example, [48][49][50][51][52][53][54][55][56][57][58]). On the other hand, some authors have studied both the non-relativistic and relativistic bound states with some potential models such as Cornell [59], harmonic oscillator [60], sum of harmonic oscillator and Cornell [61], the superposition of pseudo-harmonic, linear and Columbic potential forms [62], the Coulomb plus linear [63], the anharmonic oscillator [64], the Hulthen [65], the Coulomb-like [66] and the Killingbeck potentials [67] in the presence of the external magnetic and AB flux fields.…”

“…Also, in recent years, the exact analytical solutions of the Dirac equation have been extensively obtained, by using various methods in the presence of the spin and p-spin symmetries (see, for example, [48][49][50][51][52][53][54][55][56][57][58]). On the other hand, some authors have studied both the non-relativistic and relativistic bound states with some potential models such as Cornell [59], harmonic oscillator [60], sum of harmonic oscillator and Cornell [61],…”

On the 2D Dirac oscillator in the presence of vector and scalar potentials in the cosmic string spacetime in the context of spin and pseudospin symmetries

“…γ ϕ = e ϕ 0 γ 0 + e ϕ 1 γ 1 + e ϕ 2 γ 2 , = −γ 1 sin ϕ + γ 2 cos ϕ. (16) Given the fact that the matrices in the curved space satisfy the condition ∇ µ γ µ = 0, i.e., they are covariantly constant, for the specific basis tetrad (9), the affine spin connection is found to be…”

“…The spin symmetry has been identified by studying heavy-light mesons [4], single antinucleon spectra [5] and dynamics of a light quark (antiquark) in the field of a heavy antiquark (quark) [3] while that the pseudo-spin symmetry occurs in the motion of nucleons [3,6]. In recent studies, both the spin and the pseudo-spin symmetries appear in several aspects concerning, for instance, the supersymmetry [7,8], the Hartree-Fock theory [9], the electrons in graphene [10] and the interaction with a class of scalar and vector potentials [11][12][13][14][15][16][17][18]. An important physical system that can be studied by including such terms of interactions in the Dirac equation is the Dirac oscillator [19] (for a detailed description of this model see Ref.…”

Investigation of bound state energy spectra for fermionic particles in the presence of ultra generalized exponential hyperbolic potential model

“…If it is pseudo-spin symmetry; it has been suggested to examine properties such as deformations in core structures [9], identical bands [10][11][12], magnetic moment [13][14][15] and active-shell model [16]. In the literature, the solutions of the Dirac equation for some potential models under spin and pseudo-spin symmetries have been investigated by many researchers via different methods such as standard, asymptotic iteration, supersymmetric potential, Nikiforov Uvarov method [17][18][19][20][21][22][23][24][25][26][27][28].…”