Solution of the relativistic Dirac–Hulthén problem

  title={Solution of the relativistic Dirac–Hulth{\'e}n problem},
  author={Abdulaziz D. Alhaidari},
  journal={Journal of Physics A},
The one-particle three-dimensional Dirac equation with spherical symmetry is solved for the Hulthen potential. The s-wave relativistic energy spectrum and two-component spinor wavefunctions are obtained analytically. Conforming to the standard feature of the relativistic problem, the solution space splits into two distinct subspaces depending on the sign of a fundamental parameter in the problem. Unique and interesting properties of the energy spectrum are pointed out and illustrated… 

Figures from this paper

Approximate solutions of Klein–Gordon and Dirac equations in the presence of the Hulthén potential

The relativistic generalization of the screened potential problem is given. The Klein–Gordon and Dirac equations in the presence of the Hulthén potential V(r)=−αδe−δr/(1−e−δr) are solved by using the

The Relativistic Scattering States of the Hulthén Potential with an Improved New Approximate Scheme to the Centrifugal Term

The approximately analytical scattering state solutions of the l-wave Klein-Gordon equation with the unequal scalar and vector Hulthén potentials are carried out by an improved new approximate scheme

Approximate path integral solution for a Dirac particle in a deformed Hulthén potential

The problem of a Dirac particle moving in a deformed Hulthen potential is solved in the framework of the path integral formalism. With the help of the Biedenharn transformation, the construction of a


We introduce coupling to three-vector potential in the (3+1)-dimensional Dirac equation. The potential is noncentral (angular-dependent) such that the Dirac equation separates completely in spherical

Any l-state improved quasi-exact analytical solutions of the spatially dependent mass Klein–Gordon equation for the scalar and vector Hulthén potentials

We present a new approximation scheme for the centrifugal term to obtain a quasi-exact analytical bound state solution within the framework of the position-dependent effective mass radial

Bound States of the Klein-Gordon for Exponential-Type Potentials in D-Dimensions

The approximate analytic bound state solutions of the Klein-Gordon equation with equal scalar and vector exponential-type potentials including the centrifugal potential term are obtained for any

Systematical approach to the exact solution of the Dirac equation for a deformed form of the Woods–Saxon potential

The exact solution of the Dirac equation for a deformed form of the Woods–Saxon potential is obtained for the s-wave relativistic energy spectrum. The energy eigenvalues and two-component spinor

Approximate analytical solutions of the pseudospin symmetric Dirac equation for exponential‐type potentials

The solvability of The Dirac equation is studied for the exponential‐type potentials with the pseudospin symmetry by using the parametric generalization of the Nikiforov–Uvarov method. The energy



Solution of the Dirac Equation with Special Hulthén Potentials

The Dirac equation for the special case of a spinor in the relativistic potential with the even and odd components related by a constraint is solved exactly when the even component is chosen to be

On the relativistic two-point Green's function

Using a recently developed approach for solving the three dimensional Dirac equation with spherical symmetry, we obtain simple representations for the Green's function of the Dirac-Oscillator and

Solution of the Dirac Equation for Potential Interaction

An effective approach for solving the three-dimensional Dirac equation for spherically symmetric local interactions, which we have introduced recently, is reviewed and consolidated. The merit of the

Exact solution of the Schrodinger and Klein-Gordon equations for generalised Hulthen potentials

For the class of generalised Hulthen s-wave potentials VGH(p)(r)= Sigma i=1p giai exp(- gamma ir)/(1- Sigma j=1p aj exp(- gamma jr), p>or=1, the exact solution is presented for both the Schrodinger

Path-integral treatment of the Hulthén potential.

  • CaiInomata
  • Physics, Mathematics
    Physical review. A, General physics
  • 1986
An exact path-integral treatment of the s states for the Hulth\'en potential is presented. A procedure of the nontrivial change of variable accompanied by the local time rescaling is given in detail.

Relativistic Quantum Mechanics

In this text the authors develop a propagator theory of Dirac particles, photons, and Klein-Gordon mesons and per- form a series of calculations designed to illustrate various useful techniques and

Practical Quantum Mechanics

Part I: One-Body Problems without Spin. One-Dimensional Problems. Problems of Two or Three Degrees of Freedom without Spherical Symmetry. The Angular Momentum. Potentials of Spherical Symmetry. The

ERRATUM: Dirac equation with Hulthen potential: an algebraic approach

The energy levels of the Dirac equation with scalar and vector Hulthen type potentials are obtained by means of algebraic perturbation calculations which are based upon the dynamical group structure