Related papers: Solution of the wave equation in a tridiagonal rep…
In this paper we explore the possibility for solving the 3D Maxwell's equations in the presence of nonlinear and/or inhomogeneous material response. We propose using a hybrid approach which combines a bound- ary integral representation with…
We review an explicit approach to obtaining numerical solutions of the Schr\"odinger equation that is conceptionally straightforward and capable of significant accuracy and efficiency. The method and its efficacy are illustrated with…
A transformation method is applied to the second order ordinary differential equation satisfied by orthogonal polynomials to construct a family of exactly solvable quantum systems in any arbitrary dimensional space. Using the properties of…
The irreducible representations of the extended Galilean group are used to derive infinite sets of symmetric and asymmetric second-order differential equations with constant coeffcients. All derived equations are local and their Lagrangians…
The transfer-matrix methodology is used to solve linear systems of differential equations, such as those that arise when solving Schr\"odinger's equation, in situations where the solutions of interest are in the continuous part of the…
We show that, given any static spacetime whose spatial slices are asymptotically Euclidean (or, more generally, asymptotically conic) manifolds modeled on the large end of the Schwarzschild exterior, there exist stationary solutions to the…
A numerical algorithm to solve the spectral problem for arbitrary self-adjoint extensions of 1D regular Schroedinger operators is presented. It is shown that the set of all self-adjoint extensions of 1D regular Schroedinger operators is in…
The Self-Adjoint Extension in the Schrodinger equation for potentials behaved as an attractive inverse square at the origin is critically reviewed. Original results are also presented. It is shown that the additional non-regular solutions…
An analytical approach to quantum mechanical wave packet dynamics of laser-driven particles is presented. The time-dependent Schroedinger equation is solved for an electron exposed to a linearly polarized plane wave of arbitrary shape. The…
A new method of solution is proposed for solution of the wave equation in one space dimension with continuously-varying coefficients. By considering all paths along which information arrives at a given point, the solution is expressed as an…
Using the Tridiagonal Representation Approach, we obtain solutions (energy spectrum and corresponding wavefunctions) for a new five-parameter potential box with inverse square singularity at the boundaries.
This work is devoted to infinite-energy solutions of semi-linear wave equations in unbounded smooth domains of $\mathbb{R}^3$ with fractional damping of the form $(-\Delta_x+1)^\frac{1}{2}\partial_t u$. The work extends previously known…
Single-particle resonance parameters and wave functions in spherical and deformed nuclei are determined through analytic continuation in the potential strength. In this method, the analyticity of the eigenvalues and eigenfunctions of the…
It has been found a simple procedure for the general solution of the time-independent Schr\"odinger equation (SE) with the help of quantization of potential area in one dimension without making any approximation. Energy values are not…
This paper develops an explicit spectral representation for solutions of a one-dimensional linear wave equation with a constant time delay. The model is considered on a bounded interval with non-homogeneous Dirichlet boundary data and a…
We have developed a new family of limited-diffraction electromagnetic X-shaped waves based on the scalar "X waves" discovered previously. These waves are diffraction-free in theory and particle-like (wave packets), in that they maintain…
The exactly solvable model of quasi-conical quantum dot, having a form of spherical sector is proposed. Due to the specific symmetry of the problem the separation of variables in spherical coordinates is possible in the one-electron…
It is shown that in the case of the one-particle one-dimensional scattering problem for a given time-independent potential, for each state of the whole quantum ensemble of identically prepared particles, there is an unique pair of…
We present a refinement of the Spectral Method by incorporating an optimization method into it and generalize it to two space dimensions. We then apply this Refined Spectral Method as an extremely accurate technique for finding the bound…
Exact solutions to the d-dimensional Schroedinger equation, d\geq 2, for Coulomb plus harmonic oscillator potentials V(r)=-a/r+br^2, b>0 and a\ne 0 are obtained. The potential V(r) is considered both in all space, and under the condition of…