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The Klein-Gordon equation in D-dimensions for a recently proposed Kratzer potential plus ring-shaped potential is solved analytically by means of the conventional Nikiforov-Uvarov method. The exact energy bound-states and the corresponding…
An approximate bound state solution of the Klein-Gordon equation is derive analytically for the 3-dimensional space with a combination framework of linear plus modified Yukawa Potential (LIMYP) using the Nikiforov-Uvarov (N-U) method for…
In this paper, we solve the D-dimensional Schr\"odinger equation with hyperbolic Poschl-Teller potential plus a generalized ring-shaped potential. After the separation of variable in the hyperspherical coordinate. We used Nikiforov-Uvarov…
We consider the radial Schr\" odinger equation with the pseudo-Gaussian potential. By making an ansatz to the solution of the eigenvalue equation for the associate Hamiltonian, we arrive at the general exact eigenfunction. The values of…
An approximate solution of the $D$-dimensional Schr$\ddot{o}$dinger equation with the modified P$\ddot{o}$schl-Teller potential is obtained with an approximation of the centrifugal term. Solution to the corresponding hyper-radial equation…
By applying the Pekeris-type approximation to deal with the (pseudo or) centrifugal term, the spin and pseudospin symmetry solutions of the Dirac equation for the Rosen-Morse potential including a Coulomb-like tensor potential with…
The Duffin Kemmer Petiau (DKP) equation is solved approximately for a vector exponential-like decaying potential with any arbitrary J state by using the Pekeris approximation. The generalized parametric Nikiforov-Uvarov (NU) method is used…
The Tietz-Hua (TH) potential is one of the very best analytical model potentials for the vibrational energy of diatomic molecules. By using the Nikiforov-Uvarov (NU) method, we have obtained the exact analytical s-wave solutions of the…
The Riccati-type nonlinear differential equation, also known as the Variable Phase Approach or Phase Function Method, is used to construct local inverse potentials for the \( ^3S_1 \) and \( ^1S_0 \) states of the deuteron. The Morse…
Using the asymptotic iteration method (AIM), we have obtained analytical approximations to the $\ell$-wave solutions of the Schr\"{o}dinger equation with the Manning-Rosen potential. The equation of energy eigenvalues equation and the…
Approximate analytical solutions of the Dirac equation are obtained for the Hellmann potential, Wei Hua potential and Varshni potential with any $\kappa$-value for the cases having the Dirac equation pseudospin and spin symmetries. Closed…
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…
We introduce an exactly solvable one-dimensional potential that supports both bound and/or resonance states. This potential is a generalization of the well-known 1D Morse potential where we introduced a deformation that preserves the finite…
The Schrodinger equation for stationary states is studied in a central potential V(r) proportional to the inverse power of r of degree beta in an arbitrary number of spatial dimensions. The presence of a single term in the potential makes…
The one-dimensional Klein-Gordon equation is solved for the PT-symmetric generalized Hulthen potential in the scalar coupling scheme. The relativistic bound-state energy spectrum and the corresponding wave functions are obtained by using…
A nonpolynomial one-dimensional quantum potential in the form of an isotonic oscillator (harmonic oscillator with a centripetal barrier) is studied. We provide the non-relativistic bound state energy spectrum E_{n} and the wave functions…
The Dirac equation is solved approximately for the Hulthen potential with the pseudospin symmetry for any spin-orbit quantum number $\kappa$ in the position-dependent mass background. Solutions are obtained reducing the Dirac equation into…
An upgraded concept of solvability of Schr\"{o}dinger-type equations is proposed. In a broader methodical context of non-perturbative quantum theory the innovation involves potentials which are piece-wise analytic yielding differential…
Exact solutions of the Schrodinger equation are obtained for the Rosen-Morse and Scarf potentials with the position-dependent effective mass by appliying a general point canonical transformation. The general form of the point canonical…
We present arguments demonstrating that the application of the Nikiforov-Uvarov polynomial method to solve the Schr\"odinger equation with the Tietz-Hua potential is valid only when $e^{-b_{h}r_{e}}\leq c_{h}<1$ and $r_{0}<r<+\infty $. In…