Related papers: Barrier penetration in a discrete basis formalism
The treatment of the time-independent Schrodinger equation in real-space is an indispensable part of introductory quantum mechanics. In contrast, the Schrodinger equation in momentum space is an integral equation that is not readily…
In this paper, a quantum dot mathematical model based on a two-dimensional Schr\"odinger equation assuming the 1/r inter-electronic potential is revisited. Generally, it is argued that the solutions of this model obtained by solving a…
We have developed the technique of a quantum wave impedance determination for the sequence of not only constant potentials but also for potentials of forms for which the solution of a Shr\"{o}dinger equation exists at least in terms of…
We apply the cell merging method to a model shallow water problem with a permeable boundary. We use a cut cell approach which is more easily and systematically scalable with different shapes of boundaries. The novel cell merging method…
Three different numerical techniques for solving a coupled channel Schroedinger equation are compared. This benchmark equation, which describes the collision between two ultracold atoms, consists of two channels, each containing the same…
We present a novel numerical method and algorithm for the solution of the 3D axially symmetric time-dependent Schr\"odinger equation in cylindrical coordinates, involving singular Coulomb potential terms besides a smooth time-dependent…
Implementing high-fidelity quantum control and reducing the effect of the coupling between a quantum system and its environment is a major challenge in developing quantum information technologies. Here, we show that there exists a…
A method for obtaining discretization formulas for the derivatives of a function is presented, which relies on a generalization of divided differences. These modified divided differences essentially correspond to a change of the dependent…
This paper presents an efficient spectral method for solving the fractional Fredholm integro-differential equations. The non-smoothness of the solutions to such problems leads to the performance of spectral methods based on the classical…
In this paper it is shown how to solve numerically eigenvalue problems associated to second order linear ordinary differential equations, containing also terms which depend on the variable. A didactic presentation of the Numerov Method is…
In this paper we consider a fully third order nonlinear boundary value problem which is of great interest of many researchers. First we establish the existence, uniqueness of solution. Next, we propose simple iterative methods on both…
This paper presents a first approach in order to design an optimal architecture to implement the Numerov method, which solves the time-independent Schroedinger equation (TISE) for one dimension. The design and simulation have been performed…
This work investigates the application of the Newton's method for the numerical solution of a nonlinear boundary value problem formulated through an ordinary differential equation (ODE). Nonlinear ODEs arise in various mathematical modeling…
This work proposes a nonlinear finite element method whose nodal values preserve bounds known for the exact solution. The discrete problem involves a nonlinear projection operator mapping arbitrary nodal values into bound-preserving ones…
Many applications like subseismic fault modeling, fractured reservoir modeling and interpretation/validation of fault connectivity involve the solution to an elliptic boundary value problem in a background medium perturbed by the presence…
Boundary integral methods for the solution of boundary value PDEs are an alternative to `interior' methods, such as finite difference and finite element methods. They are attractive on domains with corners, particularly when the solution…
A robust and general solver for the radial Schr\"odinger, Dirac, and Kohn--Sham equations is presented. The formulation admits general potentials and meshes: uniform, exponential, or other defined by nodal distribution and derivative…
We consider an initial- and boundary- value problem for the nonlinear Schr\"odinger equation with homogeneous Dirichlet boundary conditions in the one space dimension case. We discretize the problem in space by a central finite difference…
This paper proposes a novel discretization workflow for contact problems in which the discretization of the contact interface is decoupled from that of the bulk domain. This separation enables independently tailored meshes for the contact…
An error analysis of a splitting method applied to the Zakharov system is given. The numerical method is a Lie-Trotter splitting in time that is combined with a Fourier collocation in space to a fully discrete method. First-order…