The one-dimensional effective-mass Klein-Gordon equation for the real, and non-textrm{PT}-symmetric/non-Hermitian generalized Morse potential is solved by taking a series expansion for the wave function. The energy eigenvalues, and the corresponding
eigenfunctions are obtained. They are also calculated for the constant mass case.
The scattering solutions of the one-dimensional Schrodinger equation for the Woods-Saxon potential are obtained within the position-dependent mass formalism. The wave functions, transmission and reflection coefficients are calculated in terms of Heun
s function. These results are also studied for the constant mass case in detail.
The Dirac equation, with position-dependent mass, is solved approximately for the generalized Hulth{e}n potential with any spin-orbit quantum number $kappa$. Solutions are obtained by using an appropriate coordinate transformation, reducing the effec
tive mass Dirac equation to a Schr{o}dinger-like differential equation. The Nikiforov-Uvarov method is used in the calculations to obtain energy eigenvalues and the corresponding wave functions. Numerical results are compared with those given in the literature. Analytical results are also obtained for the case of constant mass and the results are in good agreement with the literature.
Exact solutions of effective radial Schr{o}dinger equation are obtained for some inverse potentials by using the point canonical transformation. The energy eigenvalues and the corresponding wave functions are calculated by using a set of mass distributions
The Dirac-Morse problem are investigated within the framework of an approximation to the term proportional to $1/r^2$ in the view of the position-dependent mass formalism. The energy eigenvalues and corresponding wave functions are obtained by using
the parametric generalization of the Nikiforov-Uvarov method for any $kappa$-value. It is also studied the approximate energy eigenvalues, and corresponding wave functions in the case of the constant-mass for pseudospin, and spin cases, respectively.
The energy eigenvalues and the corresponding eigenfunctions of the one-dimensional Klein-Gordon equation with q-parameter Poschl-Teller potential are analytically obtained within the position-dependent mass formalism. The parametric generalization of
the Nikiforov-Uvarov method is used in the calculations by choosing a mass distribution.
Dirac equation is solved for some exponential potentials, hypergeometric-type potential, generalized Morse potential and Poschl-Teller potential with any spin-orbit quantum number $kappa$ in the case of spin and pseudospin symmetry, respectively. We
have approximated for non s-waves the centrifugal term by an exponential form. The energy eigenvalue equations, and the corresponding wave functions are obtained by using the generalization of the Nikiforov-Uvarov method.
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 eigenvalue equation, and the corresponding Dirac spino
rs for Morse, Hulthen, and q-deformed Rosen-Morse potentials are obtained within the framework of an approximation to the spin-orbit coupling term, so the solutions are given for any value of the spin-orbit quantum number $kappa=0$, or $kappa eq 0$.
The Klein-Gordon equation is solved approximately for the Hulth{e}n potential for any angular momentum quantum number $ell$ with the position-dependent mass. Solutions are obtained reducing the Klein-Gordon equation into a Schr{o}dinger-like differen
tial equation by using an appropriate coordinate transformation. The Nikiforov-Uvarov method is used in the calculations to get an energy eigenvalue and and the wave functions. It is found that the results in the case of constant mass are in good agreement with the ones obtained in the literature.
The effective mass Klein-Gordon equation in one dimension for the Woods-Saxon potential is solved by using the Nikiforov-Uvarov method. Energy eigenvalues and the corresponding eigenfunctions are computed. Results are also given for the constant mass case.
