Exact Solutions of Dirac Equation With Hartmann Potential by Nikiforov–uvarov Method

Abstract

We investigate the exact solution of the Dirac equation for the Hartmann potential. The radial and polar parts of the Dirac equation are solved by Nikiforov-Uvarov method. The bound state energy eigenvalues and the corresponding two-component spinor wave functions of the Dirac particles are obtained.

Dirac Equation in the Presence of Hartmann and Ring-Shaped Oscillator Potentials

“…The relativistic parameter will be restricted by ≥ 0 for > 0 and −1/4 ≤ ≤ 0 for −1 < < 0. Since there is term of + + 1 in energy spectrum and for = + 1 singularity happens in the wave function, in Generalized Laguerre polynomials related to differential equation (16), parameter is transformed to − −1. Thus energy spectrum will be restricted and the problem of singularity will disappear.…”

“…the radial wave function is considered to differential equation (16) as follows: where = 2 /2( + + 1) and 0 < < +∞. The wave function that is satisfied in Schrödinger-like equation must be physically acceptable.…”

“…There are some noncentral separable potentials in spherical coordinates which are of considerable interest and are practical in the branches of science such as chemistry and nuclear physics. Hartmann potential introduced by Hartmann is one of the noncentral potentials, which can be realized by adding a potential proportional to Coulomb potential [11][12][13][14][15][16]. This potential was suggested to describe the energy spectrum of Ring-Shaped Potential obtained by replacing the Coulomb part of Hartmann potential with a Harmonic Oscillator term and that is called a Ring-Shaped Oscillator Potential, which is investigated to find discrete spectrum and integrals of motions [17][18][19][20][21][22].…”

Solutions of D-dimensional Schrodinger equation for Woods–Saxon potential with spin–orbit, coulomb and centrifugal terms through a new hybrid numerical fitting Nikiforov–Uvarov method

“…Adding the coulomb potential (here for r \ R C ; R C = spherical nucleus radius) and solution of the Schrodinger equation by NikiforovUvarov method is the main goal of the present work. In our previous works we have used the NU method to solve the Schrodinger equation with different potentials such as angle-dependent potential [4], Energy-dependent potential [5]; Dirac equation with NU method such as Hartmann potential [6]; Duffin-Kemmer-Petiau (DKP) equation with NU method such as Woods-Saxon potential [7], Hulthen vector potential [8] and Klein-Gordon equation with NU method such as energy-dependent potential [9]. Here, we have extended the Ref.…”

Approximate Relativistic Solutions for a New Ring-Shaped Hulthén Potential

“…usually encountered in physics such as the radial and angular parts of the Schrödinger, KG and Dirac equations [36][37][38][39][40].…”