Dirac Equation with Unequal Scalar and Vector Potentials under Spin and Pseudospin Symmetry

Abstract

An approximate solution of the Dirac equation in the D-dimensional space is obtained under spin and pseudospin symmetry limits for the scalar and vector inversely quadratic Yukawa potential within the framework of parametric Nikiforov-Uvarov method using a suitable approximation scheme to the spin-orbit centrifugal term. The two components spinor of the wave function and their energy equations are fully obtained. Some numerical results are obtained for the energy level with various dimensions (D), quantum number (n), vector potential 0 V and scalar potential 0 S. The results obtained under spin symmetry using either 0 V or 0 S are equal to the results obtained using 00 VS . But under the pseudospin symmetry, the results obtained using 0 V or 0 S are not equal to the results obtained using 00 VS  .

Any l-State Solutions of the Schrodinger Equation for q-Deformed Hulthen Plus Generalized Inverse Quadratic Yukawa Potential in Arbitrary Dimensions

“…Many advanced mathematical methods have been used to solve it. Among the most popular methods are Nikiforov-Uvarov method (NU) [2][3][4][5][6][7][8][9][10], asymptotic iteration method (AIM) [11][12][13][14][15][16], supersymmetric shape invariance approach (SUSY QM) [17][18][19][20][21][22], factorization method [23], exact/proper quantization rule [24][25][26], 1/N shifted expansion method [27] and Modified Factorisation Method [28][29] which could help to obtain approximate solutions of these wave equations in the presence of a suitable approximation scheme.…”