Approximate bound states of the Dirac equation with some physical quantum potentials

Abstract

The approximate analytical solutions of the Dirac equations with the reflectionless-type and Rosen-Morse potentials including the spin-orbit centrifugal (pseudo-centrifugal) term are obtained.Under the conditions of spin and pseudospin (pspin) symmetry concept, we obtain the bound state energy spectra and the corresponding two-component upper-and lower-spinors of the two Dirac particles by means of the Nikiforov-Uvarov (NU) method in closed form. The special cases of the s-wave κ = ±1 (l = l = 0) Dirac equation and the non-relativistic limit of Dirac equation are briefly studied.

Solutions of N-dimensional Schrödinger equation with Morse potential via Laplace transforms

“…Solutions of the Schrödinger equation for the sate ℓ = 0 has been found in [4]- [6]. However, due to complexity of the case ℓ = 0, the wave equation can only be solved by using perturbation and approximation.…”

Supersymmetric analysis of the Dirac-Weyl operator within $\mathcal{PT}$PT symmetry

“…The properties of the intertwining relations in pseudo-supersymmetric quantum mechanics are then used to obtain a third Hamiltonian linked with those partner Hamiltonians where we have also formed the intertwining operators η 1 , η 2 . We have seen that H given by (31) may be the one of the Hamiltonian whose possible effective potentials are given by (38), (39), (40) and (41). Hereafter we have employed the polynomial procedures called as Nikiforov-Uvarov method to find the solutions of H and obtained the energy spectra and eigenfunctions.…”

The quadratic plus the tensor potentials for particle with 1/2‐spin via L2 method under the spin symmetry

“…In recent years, there have been an increase in searching for analytic solution of the Dirac equation. For example, see [30][31][32][33][34][35]. The quadratic potential [36] is as…”