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

  title={Dirac Equation in the Presence of Hartmann and Ring-Shaped Oscillator Potentials},
  author={Zahra Bakhshi},
  journal={Advances in High Energy Physics},
  • Z. Bakhshi
  • Published 4 July 2018
  • Physics
  • Advances in High Energy Physics
The importance of the energy spectrum of bound states and their restrictions in quantum mechanics due to the different methods have been used for calculating and determining the limit of them. Comparison of Schrödinger-like equation obtained by Dirac equation with the nonrelativistic solvable models is the most efficient method. By this technique, the exact relativistic solutions of Dirac equation for Hartmann and Ring-Shaped Oscillator Potentials are accessible, when the scalar potential is… 
3 Citations

Bound states of Dirac equation using the proper quantization rule

Using the proper quantization rule, we investigate the exact solution of Dirac equation for Hartmann and the ring-shaped non-spherical harmonic oscillator potentials under the condition of equal

Many-body quantum system in the presence of solvable potential

This article introduces a four-particle quantum system presented with a discrete energy spectrum, including harmonic potential and three-body interaction potential. By defining each particle’s Jacobi

Relativistic potentials with rational extensions

In this paper, we construct isospectral Hamiltonians without shape-invariant potentials for the relativistic quantum mechanical potentials such as the Dirac oscillator and hydrogen-like atom.



Energy spectra of Hartmann and ring-shaped oscillator potentials using the quantum Hamilton–Jacobi formalism

In the present work, we apply the exact quantization condition, introduced within the framework of Padgett and Leacock's quantum Hamilton–Jacobi formalism, to angular and radial quantum action

Dynamical invariance algebra of the Hartmann potential

The 'accidental' degeneracy occurring in the quantum mechanical treatment of the ring-shaped potential V=- eta sigma 2r-1+1/2q eta 2 sigma 2(r sin theta )-2 is explained by constructing an su(2)


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

Quantum correction in exact quantization rules

An exact quantization rule for the Schrodinger equation is presented. In the exact quantization rule, in addition to Nπ, there is an integral term, called the quantum correction. For the exactly

Exact Solution of Klein-Gordon with the Pöschl-Teller Double-Ring-Shaped Coulomb Potential

Analytical solution of the Klein Gordon equation under the equal scalar and vector Poschl Teller double-ring-shaped Coulomb potentials is obtained. We have used the Nikiforov Uvarov method in our

Exact motion in noncentral electric fields

We study the problem of the motion of a charged particle in noncentral potentials of the type f(θ)/r2 + V(r). Newton's and Schrodinger's mechanics are considered. Exact solutions exist if V(r)=−H/r

Scattering and bound states for a class of non-central potentials

We obtain L2-series solutions of the three-dimensional Schrodinger wave equation for a large class of non-central potentials that includes, as special cases, the Aharonov–Bohm, Hartmann and magnetic

Oscillator strengths based on the Möbius square potential under Schrödinger equation

By applying the NU method and an approximation to the centrifugal term, we have solved the Schrödinger equation in D-dimensions for the Möbius square potential which in some particular cases gives

Algebraic approach to pseudospin symmetry for the Dirac equation with scalar and vector modified Pöschl-Teller potentials

By the algebraic method we study the approximate solution to the Dirac equation with scalar and vector modified Pöschl-Teller (MPT) potentials carrying pseudospin symmetry. The transcendental energy