Exact Solutions of Klein--Gordon Equation with Scalar and Vector Rosen--Morse-Type Potentials

We obtain an exact analytical solution of the Klein Gordon equation for the equal vector and scalar Rosen Morse and Eckart potentials as well as the parity-time （PT） symmetric version of the these potentials by using the asymptotic iteration method. Although these PT symmetric potentials are non-Hermitian, the corresponding eigenvalues are real as a result of the PT symmetry.     

Exact Solutions of the Dirac Equation for an Electron in a Magnetic Field with Shape Invariant Method

Based on the shape invariance property we obtain exact solutions oI the Dirac equation for an electron moving in the presence of a certain varying magnetic field, then we also show its non-relativistic limit.     

具有Poschl-Teller型标量势与矢量势的Klein-Gordon方程和Dirac方程的束缚态

给出了具有Poschl-Teller型标量势与矢量势的Klein-Gordon方程和Dirac方程的s波束缚态解.     

Supersymmetry and Solution of Dirac Equation with Vector and Scalar Potentials

The Dirac equations with vector and scalar potentials of the Coulomb types in two and three dimensions are solved using the supersymmetric quantum mechanics method. For the system of such potentials, the analytical expressions of the matrix dements for both position and momentum operators are obtained.     

Bound states of the Dirac equation for a class of effective quadratic plus inversely quadratic potentials

The Dirac equation is exactly solved for a pseudoscalar linear plus Coulomb-like potential in a two-dimensional world. This sort of potential gives rise to an effective quadratic plus inversely quadratic potential in a Sturm-Liouville problem, regardless the sign of the parameter of the linear potential, in sharp contrast with the Schrödinger case. The generalized Dirac oscillator already analyzed in a previous work is obtained as a particular case.     

An Improvement of the Asymptotic Iteration Method for Exactly Solvable Eigenvalue Problems

We derive a formula that simplifies the original asymptotic iteration method formulation to find the energy eigenvalues for the analytically solvable cases. We then show that there is a connection between the asymptotic iteration and the Nikiforo-Uvarov methods, which both solve the second order linear ordinary differential equations analytically.     

Extension of PT-symmetric quantum mechanics to the Dirac theory with position-dependent mass

We present a new method to construct the exactly solvable PT-symmetric potentials within the framework of the position-dependent effective mass Dirac equation with the vector potential coupling scheme in 1 + 1 dimensions. In order to illustrate the procedure, we produce three PT-symmetric potentials as examples, which are PT-symmetric harmonic oscillator-like potential, PT-symmetric potential with the form of a linear potential plus an inversely linear potential, and PT-symmetric kink-like potential, respectively. The real relativistic energy levels and corresponding spinor components for the bound states are obtained by using the basic concepts of the supersymmetric quantum mechanics formalism and function analysis method.     

Dirac equation with scalar and vector quadratic potentials and Coulomb-like tensor potential

It is shown that the Dirac equation with scalar and vector quadratic potentials and a Coulomb-like tensor potential can be solved exactly. The bound state solutions for equal vector and scalar potentials are obtained. The limit of zero tensor coupling is investigated. The case of equal vector and scalar potentials with opposite sign is also studied. The pseudospin symmetry and its breaking by the tensor interaction are discussed.     

Exact solution of the Dirac equation with the Mie-type potential under the pseudospin and spin symmetry limit

We investigate the exact solution of the Dirac equation for the Mie-type potentials under the conditions of pseudospin and spin symmetry limits. The bound state energy equations and the corresponding two-component spinor wave functions of the Dirac particles for the Mie-type potentials with pseudospin and spin symmetry are obtained. We use the asymptotic iteration method in the calculations. Closed forms of the energy eigenvalues are obtained for any spin-orbit coupling term κ. We also investigate the energy eigenvalues of the Dirac particles for the well-known Kratzer-Fues and modified Kratzer potentials which are Mie-type potentials.     

An Alternative Method for Calculating Bound-State of Energy Eigenvalues of Klein-Gordon for Quasi-exactly Solvable Potentials

We obtain the bound-state energy of the Klein-Gordon equation for some examples of quasi-exactly solvable potentials within the framework of asymptotic iteration method （AIM）. The eigenvalues are calculated for type- 1 solutions. The whole quasi-exactly solvable potentials are generated from the defined relation between the vector and scalar potentials.     

Analytical approximation to the solution of the Dirac equation with the Eckart potential including the spin-orbit coupling term

By using the supersymmetric WKB approximation approach and the functional analysis method, we solve approximately the Dirac equation with the Eckart potential for the arbitrary spin-orbit quantum number κ. The bound state energy eigenvalues and the associated two-component spinors of the Dirac particles are obtained approximately.     

Dirac Equation and Some Quasi-Exact Solvable Potentials in the Turbiner's Classification

In this paper quasi-exact solvability(QES)of Dirac equation with some scalar potentials based on sl(2)Lie algebra is studied.According to the quasi-exact solvability theory,we construct the configuration of the classes II,IV,V,and X potentials in the Turbiner’s classification such that the Dirac equation with scalar potential is quasi-exactly solved and the Bethe ansatz equations are derived in order to obtain the energy eigenvalues and eigenfunctions.     

Quasi-exact solvability of Dirac-Pauli equation and generalized Dirac oscillators

In this paper we demonstrate that neutral Dirac particles in external electric fields, which are equivalent to generalized Dirac oscillators, are physical examples of quasi-exactly solvable systems. Electric field configurations permitting quasi-exact solvability of the system based on the sl(2) symmetry are discussed separately in the spherical, cylindrical, and Cartesian coordinates. Some exactly solvable field configurations are also exhibited.     

Dirac Equation and Ground State of Solvable Potentials: Supersymmetry Method

The supersymmetry in non-relativistic quantum mechanics is applied as an algebraic method to obtain the solutions of the Dirac equation with spherical symmetry electromagnetic potentials. We show that some of the superpotentials related to ground state of the solvable potentials in non-relativistic quantum mechanics can be used for studying of the Dirac equation.     

Quasi-exact solvability of Dirac equation with Lorentz scalar potential

We consider exact/quasi-exact solvability of Dirac equation with a Lorentz scalar potential based on factorizability of the equation. Exactly solvable and sl (2)-based quasi-exactly solvable potentials are discussed separately in Cartesian coordinates for a pure Lorentz potential depending only on one spatial dimension, and in spherical coordinates in the presence of a Dirac monopole.     

Dirac Equation for Scalar,Vector and Tensor Generalized Cornell Interaction

We consider spin and pseudospin symmetry limits of Dirac equation in the presence of scalar, vector and tensor generalized Cornell interaction and report the solutions via the quasi-exact analytical ansatz approach.     

Dirac Equation and Some Quasi-Exact Solvable Potentials in the Turbiner’s Classification

In this paper quasi-exact solvability (QES) of Dirac equation with some scalar potentials based on sl(2) Lie algebra is studied. According to the quasi-exact solvability theory, we construct the configuration of the classes II, IV, V, and X potentials in the Turbiner's classification such that the Dirac equation with scalar potential is quasi-exactly solved and the Bethe ansatz equations are derived in order to obtain the energy eigenvalues and eigenfunctions.     

Oscillator model for the relativistic fermion-boson system

The solvable quantum mechanical model for the relativistic two-body system composed of spin-1/2 and spin-0 particles is constructed. The model includes the oscillator-type interaction through a combination of Lorentz-vector and Lorentz-tensor potentials. The analytical expressions for the wave functions and the order of the energy levels are discussed.     

Analytic Advantages of Spherically Symmetric Step-Function Potentials in the Dirac Equation with Scalar and Fourth Component of Vector Potential

The root mean square radii of the particle orbits are calculated (semi)analyticallyfor every bound state, using the Dirac equation with a scalar potentialU _s andfourth component of a vector potentialU _v in the case of a spherically symmetricstep-function shape with the same radiusR for these potentials. In addition, a(semi)analytic expression of the expectation value of the corresponding potentialenergy operator is derived. For the above quantities, expressions of the energyeigenvalues in terms of the potential parameters are needed and approximateformulas may be used in certain cases. This study emphasizes the analyticadvantages of the relativistic, spherically symmetric step-function potential model.Its applicability is discussed in connection with a problem of physical interest,namely that of the motion of a particle in hypernuclei.     

Bound States of the Klein-Gordon Equation With Vector and Scalar Wood-Saxon Potentials

In this paper,simultaneously considering the variation of classical mass and the relativistic effect of mass variation with velocity,a relativistic four-covariant equation of variable mass body is built.And the physical meaning of