Dirac Equation with Mixed Scalar–Vector–Pseudoscalar Linear Potential under Relativistic Symmetries

Abstract

In the presence of spin and pseudospin (p-spin) symmetries, the approximate analytical bound states of the Dirac equation, which describes the motion of a spin-1/2 particle in 1+1 dimensions for mixed scalarvector-pseudoscalar linear potential are investigated. The Nikiforov-Uvarov (NU) method is used to obtain energy eigenvalues and corresponding wave functions in their closed forms.

Dynamics of the Dirac Particle in an Anisotropic Rainbow Universe

“…Subsequently, Eq. 16 is reduced to the following form by setting 𝛹 = 𝑡 −1 𝜓 to eliminate the contribution from the spinor connections [𝛾 (0) 𝜕 0 + 𝑔 𝑡𝑓 (𝛾 (1) 𝜕 1 + 𝛾 (2) 𝜕 2 ) + 𝑔 𝑓 𝛾 (3) By using 𝛾 (3) 𝛾 (0) 𝛾 (3) 𝛾 (0) = 1, Eq. 17 can be easily expressed as a sum of two first-order differential operators after some mathematical steps…”

“…To overcome such a challenge, Dirac proposed a first-order relativistic wave equation that plays an important role in many branches including those in nuclear and high energy physics. It is commonly believed that this idea is the most effective mathematical method to analyze the relativistic quantum mechanical behavior of the spin-1 2 particles (electron, proton, and their corresponding antiparticles) [2]. Therefore, one can easily see that there are lots of papers where some solutions of the Dirac equation are illustrated in various spacetimes [3][4][5][6][7].…”

Spin symmetry in the Dirac sea derived from the bare nucleon–nucleon interaction

“…[8] and its connection to spin symmetry was also suggested there. Since then, pseudospin symmetry has been realized as a relativistic symmetry and much work has been done to investigate its origin and its properties using phenomenological single-particle Hamiltonians, relativistic mean field theory, or relativistic Hartree-Fock (RHF) theory [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26].If one starts with a Dirac Hamiltonian, there exist single-particle states not only with positive energy but also with negative energy, states in the so-called Dirac sea. It was shown in Ref.[27] that the pseudospin symmetry in the positive spectrum has the same origin as the spin symmetry in the Dirac sea.…”

“…[8] and its connection to spin symmetry was also suggested there. Since then, pseudospin symmetry has been realized as a relativistic symmetry and much work has been done to investigate its origin and its properties using phenomenological single-particle Hamiltonians, relativistic mean field theory, or relativistic Hartree-Fock (RHF) theory [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26].…”