Bound States for Pseudoharmonic Potential of the Dirac Equation with Spin and Pseudo-Spin Symmetry via Laplace Transform Approach

Abstract

Bound state solutions of the Dirac equation for the pseudoharmonic potential with spin and pseudo-spin symmetry are studied in this paper. To obtain the exactly normalized bound state wave function and energy expressions we have used the Laplace transform approach.

A Novel Exactly Theoretical Solvable of Bound States of the Dirac-Kratzer-Fues Problem with Spin and Pseudo-Spin Symmetry

“…We briefly review the differential Dirac equation of a nucleon with mass M moving in both two potentials: attractive scalar potential (19) here k ( k ) is related to the total angular momentum quantum numbers for spin symmetry l and pspin symmetry l~ as [14][15][16]:…”

“…In relativistic quantum mechanics, one of the interesting problems is to obtain exact solutions of the Klein-Gordon equation (spin zero particle) and Dirac equation (spin ½ particle) at high energy, much interest in providing analytic solutions to the relativistic equations in many fields of Physics and Chemistry for different central and non central potentials [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. The quantum structure based to the ordinary canonical commutations relations in both Schrödinger and Heisenberg (the operators are depended on time) pictures, respectively (Natural units (3) here Ĥ denote to the ordinary quantum Hamiltonian operator.…”

“…The quantum structure based to the ordinary canonical commutations relations in both Schrödinger and Heisenberg (the operators are depended on time) pictures, respectively (Natural units (3) here Ĥ denote to the ordinary quantum Hamiltonian operator. In addition, for spin ½ particles described by the Dirac equation, experiment tells us that must satisfy Fermi Dirac statistics obey the restriction of Pauli, which imply to gives the only non-null equal-time anti-commutator for field operators as follows: [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] Revised: 2016-11-16 doi:10.18052/www.scipress.com/IFSL. 10.8 Accepted: 2016-11-30 2016SciPress Ltd., Switzerland Online: 2016 SciPress applies the CC- .…”

“…In particularly, the study of Kratzer-Fues potential has now become a very interest field due to their applications in different fields [16]. The main motivation of this work is to study and obtaining an analytic expression for the eigenenergies of a (m.k.f.)…”

“…This work is organized as follows: In section 2, we briefly review the Dirac equation with Kratzer-Fues potential on based to Refs. [14][15][16]. The Section 3, devoted to studying the three deformed Dirac equation by applying Bopp's shift method.…”