Exact solutions of the Dirac equation with Pschl-Teller double-ring-shaped Coulomb potential via the Nikiforov-Uvarov method

Exact analytical solutions of the Dirac equation are reported for the Poschl-Teller double-ring-shaped Coulomb potential.The radial,polar,and azimuthal parts of the Dirac equation are solved using the Nikiforov-Uvarov method,and the exact bound-state energy eigenvalues and corresponding two-component spinor wavefunctions are reported.

Pseudospin symmetric solutions of the Dirac equation with the modified Rosen-Morse potential using Nikiforov-Uvarov method and supersymmetric quantum mechanics approach

Employing the Pekeris-type approximation to deal with the pseudo-centrifugal term,we analytically study the pseudospin symmetry of a Dirac nucleon subjected to equal scalar and vector modified Rosen-Morse potential including the spin-orbit coupling term by using the Nikiforov-Uvarov method and supersymmetric quantum mechanics approach.The complex eigenvalue equation and the total normalized wave functions expressed in terms of Jacobi polynomial with arbitrary spin-orbit coupling quantum number k are presented under the condition of pseudospin symmetry.The eigenvalue equations for both methods reproduce the same result to affirm the mathematical accuracy of analytical calculations.The numerical solutions obtained for different adjustable parameters produce degeneracies for some quantum number.

Approximate solutions of Dirac equation with a ring-shaped Woods-Saxon potential by Nikiforov-Uvarov method

An approximate analytical solution of the Dirac equation is obtained for the ring-shaped Woods-Saxon potential within the framework of an exponential approximation to the centrifugal term. The radial and angular parts of the equation are solved by the Nikiforov-Uvarov method. The general results obtained in this work can be reduced to the standard forms already present in the literature.

Solutions of the Dirac Equation with Gravitational plus Exponential Potential

The solutions of the Alhaidari formalism of the Dirac equation for the gravitational plus exponential potential have been presented using the parametric Nikiforov-Uvarov method. The energy eigenvalues and the corresponding unnormalized eigenfunctions are obtained in terms of Laguerre polynomials.

Exact Solution of Dirac Equation with Charged Harmonic Oscillator in Electric Field: Bound States

In some quantum chemical applications, the potential models are linear combination of single exactly solvable potentials. This is the case equivalent of the Stark effect for a charged harmonic oscillator (HO) in a uniform electric field of specific strength (HO in an external dipole field). We obtain the exact s-wave solutions of the Dirac equation for some potential models which are linear combination of single exactly solvable potentials (ESPs). In the framework of the spin and pseudospin symmetric concept, we calculate analytical expressions for the energy spectrum and the corresponding two-component upper- and lower-spinors of the two Dirac particles by using the Nikiforov-Uvarov (NU) method, in closed form. The nonrelativistic limit of the solution is also studied and compared with the other works.

The spin-one Duffin Kemmer Petiau equation in the presence of pseudo-harmonic oscillatory ring-shaped potential

The Duffin-Kemmer-Petiau equation （DKP） is studied in the presence of a pseudo-harmonic oscillatory ring-shaped potential in （1 ＋ 3）-dimensional space-time for spin-one particles. The exact energy eigenvalues and the eigenfunctions are obtained using the Nikiforov-Uvarov method.

Duffin-Kemmer-Petiau equation under Hartmann ring-shaped potential

We solve the DufRn-Kemmer-Petiau（DKP） equation in the presence of Hartmann ring-shaped potential in（3＋l）-dimensional space-time.We obtain the energy eigenvalues and eigenfunctions by the Nikiforov-Uvarov（NU）method.

First attempt to overcome the disaster of Dirac sea in imaginary time step method

Efforts have been made to solve the Dirac equation with axially deformed scalar and vector WoodsSaxon potentials in the coordinate space with the imaginary time step method. The results of the singleparticle energies thus obtained are consistent with those calculated with the basis expansion method, which demonstrates the feasibility of the imaginary time step method for the relativistic static problems.

A semi-relativistic treatment of spinless particles subject to the nuclear Woods-Saxon potential

By applying an appropriate Pekeris approximation to deal with the centrifugal term, we present an approximate systematic solution of the two-body spinless Salpeter （SS） equation with the Woods-Saxon interaction potential for an arbitrary/-state. The analytical semi-relativistic bound-state energy eigenvalues and the corresponding wave functions are calculated. Two special cases from our solution are studied： the approximated SchrSdinger- Woods-Saxon problem for an arbitrary/-state and the exact s-wave （l=0）.