Spin (Pseudospin) doublet in view of energy-dependent potential

Abstract

Abstract:Behavior of Dirac particles in the presence of scalar, vector, and tensor potentials respectively represented by energy-dependent Morse and Coulomb-like potentials is examined by working out the Dirac equation under the condition of spin (pseudospin) symmetry. The closed form of the energy eigenvalue equation and corresponding wave functions in terms of hypergeometric functions are acquired by making use of the asymptotic iteration method. We investigate the effect of energy-dependent potential on both bound states and energy splitting between members of spin (pseudospin) doublets.

Solutions of the Schrödinger equation with velocity-dependent potentials:a study on Kratzer, Mie and Hulthen potentials

“…For instance, numerous authors have investigated the bound-state solutions of the Hulthen potential using various methods, including the Nikiforov-Uvarov (NU) method [19], the shifted 1/N expansion method [20], and the supersymmetry (SUSY) method [21][22][23][24], specifically for the s-wave Schrödinger equation. Furthermore, the Hulthen potential's solution has been obtained using the NU method and the Asymptotic Iteration Method (AIM) for relativistic wave equations, such as the Klein-Gordon equation [25][26][27][28][29][30][31][32], Dirac equation [33], and the Duffin-Kemmer-Petiau (DKP) equation [34]. Additionally, addressing the solutions for various angular momentum states of the Schrödinger equation for this potential has been accomplished in reference [35] through the application of AIM.…”

Arbitrary l-Solutions of the Schrodinger Equation in Arbitrary Dimensions for the Energy Dependent Generalized Inverse Quadratic Yukawa Potential

“…They can be seen in relativistic quantum mechanics considering particle in an external electromagnetic field [1]- [3]. Energy-dependent potential has been studied in nonrelativistic and relativistic quantum mechanics [4]- [10]. Recently, researchers have showed renewed interest in the study of Energy Dependent Potential (in both relativistic and non-relativistic regime), some of the study amongst others are; [11] studied the Schrödinger equation in D-dimensions for an energydependent Hamiltonian that linearly depends on energy and quadratic on the relative distance using the Nikiforov-Uvarov formalism.…”

Spin and Pseudo-Spin Symmetries in Radial Dirac Equation and Exceptional Hermite Polynomials

“…Among the physical applications, one can find models of heavy quark systems [14], semiconductors [15] and energy loss characteristics of an electron probe [16]. Accordingly, spin symmetry and pseudospin symmetry were investigated for the systems whose potential functions are energy dependent [17], [18], [19]. Energy dependent Hamiltonians first mentioned in 1927 through Pauli Schrodinger equation [20].…”