Related papers: Application of Asymptotic Iteration Method (AIM) t…
Exact solutions for vibrational levels of diatomic molecules via the Morse potential are obtained by means of the asymptotic iteration method. It is shown that, the numerical results for the energy eigenvalues of $^{7}Li_{2}$ are all in…
We have derived and analyzed the wavefunctions and energy states for an asymmetric double quantum wells, broadened due to static interface disorder effects, within well known discreet variable representation approach for solving the…
In this research work, we investigate the 2D Schrodinger equation with improved ultra-generalized exponential-hyperbolic potential (IUGE-HP) is scrutinized taking into consideration the effects external magnetic and Aharanov-Bohm (AB)…
The bound state solutions of the $D$-dimensional Schr\"{o}dinger equation for new mixed class of potential, $V(r)=\frac{V_1}{r^2}+\frac{V_2e^{-\alpha r}}{r}+V_3coth\alpha r+V_4\,,$ are studied within the framework of the Pekeris…
We extend the conforming virtual element method to the numerical resolution of eigenvalue problems with potential terms on a polytopal mesh. An important application is that of the Schrodinger equation with a pseudopotential term. This…
The original model of the infinite square well contains a vague notation infinity and therefore results some ambiguities. We investigate to obtain a functional form for the potential energy V(x). This is done by substituting back the…
Exact solution of the Schrodinger equation with deformed ring shaped potential is obtained in the parabolic and spherical coordinates. The Nikiforov-Uvarov method is used in the solution. Eigenfunctions and corresponding energy eigenvalues…
We study the problem of optimal observability and prove time asymptotic observability estimates for the Schr\"odinger equation with a potential in $L^{\infty}(\Omega)$, with $\Omega\subset \mathbb{R}^d$, using spectral theory. An elegant…
An asymptotic interation method for solving second-order homogeneous linear differential equations of the form y'' = lambda(x) y' + s(x) y is introduced, where lambda(x) \neq 0 and s(x) are C-infinity functions. Applications to Schroedinger…
We implement physics-informed neural networks (PINNs) to solve the time-independent Schr\"odinger equation for three canonical one-dimensional quantum potentials: an infinite square well, a finite square well, and a finite barrier. The PINN…
We have developed a new simple method to build the exact analytical expression of the eigenenergy as a function of the potential. The idea of our method is mainly based on the partitioning of the potential curve, solving the Schr\"odinger…
We consider a single particle which is bound by a central potential and obeys the Dirac equation in d dimensions. We first apply the asymptotic iteration method to recover the known exact solutions for the pure Coulomb case. For a…
In this paper, we develop an asymptotic expansion-regularization (AER) method for inverse source problems in two-dimensional nonlinear and nonstationary singularly perturbed partial differential equations (PDEs). The key idea of this…
Analytical solutions of the Bohr Hamiltonian are obtained in the $\gamma$-unstable case, as well as in an exactly separable rotational case with $\gamma\approx 0$, called the exactly separable Morse (ES-M) solution. Closed expressions for…
The approximate solution of Bohr-Mottelson Hamiltonian in rigid deformed nucleus case for Hulthen potential with minimal length effect was investigated using Asymptotic Iteration Method. Asymptotic Iteration Method was used to solve…
In this work, we study the exact solution of Dirac equation in the hyper-spherical coordinate under influence of separable q-Deformed quantum potentials. The q-deformed hyperbolic Rosen-Morse potential is perturbed by q-deformed non-central…
Using the recent analysis of the output of the low-energy resolvent of Schr\"odinger operators on asymptotically conic manifolds (including Euclidean space) when the potential is short-range, we produce detailed asymptotic expansions for…
In this paper we obtain asymptotic formulas of arbitrary order for the Bloch eigenvalues and Bloch functions of the Schrodinger operator of arbitrary dimension, with periodic, with respect to arbitrary lattice, potential. Moreover, we…
The present contribution concerns the computation of energy eigenvalues of a perturbed anharmonic coulombic potential with irregular singularities using a combination of the Sinc collocation method and the double exponential transformation.…
We derive exact analytical solutions of the Klein-Gordon equation for Makarov potential by means of the asymptotic iteration method. The energy eigenvalues are given in a closed form and the corresponding normalized eigenfunctions are…