Bound state solution of the Dirac equation for a new anharmonic oscillator potential

Abstract

It is shown that the Dirac equation for a new equal scalar and vector anharmonic oscillator potentials could be separated into a solvable angular equation and a radial equation. Corresponding exact solutions of bound states for the Dirac equation have been obtained. The angular solutions are the associated-Legendre polynomial and the radial solutions are expressed in terms of the confluent hypergeometric functions. Finally, the energy equation is found from the boundary condition satisfied by the radial wavefunction.

Arbitrary Wave Relativistic Bound State Solutions for the Eckart Potential

“…and comparing it with (21) of [13], and observing the relations of corresponding parameters, then (25) can be rearranged as…”

“…and for the bound states, the hypergeometric functions must be terminated with a polynomial [25], which demands…”

Solutions of the Klein-Gordon equation with equal scalar and vector harmonic oscillator plus inverse quadratic potential

“…Some of these potentials are known to play very important roles in many fields of Physics such as Molecular Physics, Solid State and Chemical Physics [21]. When a particle is in a strong potential field, the relativistic effects must be considered, leading to the relativistic quantum mechanical description of such a particle [22][23][24][25][26]. In the relativistic limit, the particle's motions are very often described using either the KG equation or the Dirac equation depending on the spin character of the particle [23][24].…”

“…When a particle is in a strong potential field, the relativistic effects must be considered, leading to the relativistic quantum mechanical description of such a particle [22][23][24][25][26]. In the relativistic limit, the particle's motions are very often described using either the KG equation or the Dirac equation depending on the spin character of the particle [23][24]. The spin-zero particles like the mesons are satisfactorily described by the KG equation while the spin-half particles such as the electrons are described by the Dirac equation.…”

Solutions of the Dirac Equation for the Davidson Potential

“…Wei and co-workers used the usual algebraic approach to solve the Dirac equation for the anharmonic oscillator potential [28]. In a recent work we want to use the algebraic technique NU to solve Dirac equation with equal scalar and vector anharmonic oscillator potential.…”