Related papers: Exact Solutions of Schrodinger Equation for a Ring…
This paper presents the exact ground state solution for a diatomic particle system with position-dependent complex mass under action of a complex Morse potential in the quantum domain. By solving the position-dependent Schr\"odinger…
We show that the Riccati form of the Schrodinger equation can be reformulated in terms of two linear equations depending on an arbitrary function G. When $G$ and the potential are polynomials, the solutions of these two equations are entire…
The radial part of the effective mass Klein-Gordon equation for the Hulthen potential is solved by making an approximation to the centrifugal potential. The Nikiforov-Uvarov method is used in the calculations. Energy spectra and the…
The matrix Numerov method provides an efficient framework for solving the time-independent Schr\"odinger equation as a matrix eigenvalue problem. However, for singular potentials such as the Coulomb interaction, the expected fourth-order…
Analytic approximants for the eigenvalues of the one-dimensional Schr\"odinger equation with potentials of the form $V(x)= Ax^a + Bx^b$ are found using a multi-point quasi-rational approximation technique. This technique is based on the use…
The non-relativistic Schrodinger equation with the linear and Coulomb potentials is solved numerically in configuration space using the relaxation method. The numerical method presented in this paper is a plain explicit Schrodinger solver…
Analytic and approximate solutions for the energy eigenvalues generated by the hyperbolic potentials $V_m(x)=-U_0\sinh^{2m}(x/d)/\cosh^{2m+2}(x/d),\,m=0,1,2,\dots$ are constructed. A byproduct of this work is the construction of polynomial…
An approximate solution of the Schrodinger equation with the Hulth$\acute{e}$n potential is obtained in D-dimensions with an exponential approximation of the centrifugal term. Solution to the corresponding hyper-radial equation is given…
In this paper, we consider the maximal estimates for the solution to an initial value problem of the linear Schroedinger equation with a singular potential. We show a result about the pointwise convergence of solutions to this special…
Using the Nikiforov Uvarov method, we obtained the eigenvalues and eigenfunctions of the Woods Saxon potential with the negative energy levels based on the mathematical approach. According to the PT Symmetric quantum mechanics, we exactly…
Asymptotics of solutions to Schroedinger equations with singular dipole-type potentials is investigated. We evaluate the exact behavior near the singularity of solutions to elliptic equations with potentials which are purely angular…
We present an application of a nonstandard approximate method---the finite-rank approximation---to solving the time-independent Schr\"odinger equation for a bound-state problem. The method is illustrated on the example of a…
In this study, inverse nodal problem is solved for p-Laplacian Schr\"odinger equation with energy-dependent potential with the Drichlet conditions. Asymptotic estimates of eigenvalues, nodal points and nodal lengths are given by using…
The exact solutions of the Schrodinger equation with the hyperbolic Scarf potential reported in the literature so far rely upon Jacobi polynomials with imaginary arguments and parameters. We here show that upon a suitable factorization…
We solve the one-dimensional Schr\"odinger equation for the bound states of two potential models with a rich structure as shown by their "spectral phase diagram". These potentials do not belong to the well-known class of exactly solvable…
We construct exact ring soliton-like solutions of the cylindrically symmetric (i.e., radial) Gross- Pitaevskii equation with a potential, using the similarity transformation method. Depending on the choice of the allowed free functions, the…
The eigenvalue problem for one-dimensional Schr\"{o}dinger equation with the rational potential is numerically solved by the operator method. We show that the operator method, applied for solving the Schr\"{o}dinger equation with the…
We consider the semilinear electromagnetic Schr\"{o}dinger equation (-i\nabla+A(x))^{2}u + V(x)u = |u|^{2^{\ast}-2}u, u\in D_{A,0}^{1,2}(\Omega,\mathbb{C}), where $\Omega=(\mathbb{R}^{m}\smallsetminus{0})\times\mathbb{R}^{N-m}$ with $2\leq…
Bound states of the power-law and logarithmic potentials are calculated using a generalized pseudospectral method. The solution of the single-particle Schr\"odinger equation in a nonuniform and optimal spatial discretization offers accurate…
We develop an approach to solving numerically the time-dependent Schrodinger equation when it includes source terms and time-dependent potentials. The approach is based on the generalized Crank-Nicolson method supplemented with an…