Related papers: Eigenvalue Problem in Two Dimension for An Irregul…
We analyze the low-lying states for a one-dimensional potential consisting of $N$ identical wells, assuming that the wells are parabolic around the minima. Matching the exact wave functions around the minima and the WKB wave functions in…
Universal low-energy properties are studied for three identical bosons confined in two dimensions. The short-range pair-wise interaction in the low-energy limit is described by means of the boundary condition model. The wave function is…
An algorithm named EigenWave is described to compute eigenvalues and eigenvectors of elliptic boundary value problems. The algorithm, based on the recently developed WaveHoltz scheme, solves a related time-dependent wave equation as part of…
In this paper, using the approximate particular solutions of Helmholtz equations, we solve the boundary value problems of Helmholtz equations by combining the methods of fundamental solutions (MFS) with the methods of particular solutions…
Exactly solvable models play an extremely important role in many fields of quantum physics. In this study, the Schr\"{o}dinger equation is applied for a solution of a two--dimensional (2D) problem for two particles interacting via Kratzer,…
Dynamical energy analysis was recently introduced as a new method for determining the distribution of mechanical and acoustic wave energy in complex built up structures. The technique interpolates between standard statistical energy…
Highly accurate closed-form approximations are given for the ground state and first excited state wavefunctions and energies for a nonrelativistic particle in a one-dimensional double square well potential with a square barrier in between…
In this paper we study the existence of solutions of a one-dimensional eigenvalue problem $-\left(|\phi_x|^{p-2}\phi_x\right)_x=\lambda \left(|\phi|^{q-2}\phi-f(\phi)\right)$ such that $\phi(0)=\phi(1)=0$, where $p,q>1$, $\lambda$ is a…
Numerically solving the 2D Helmholtz equation is widely known to be very difficult largely due to its highly oscillatory solution, which brings about the pollution effect. A very fine mesh size is necessary to deal with a large wavenumber…
We consider the initial-value problem for a one-dimensional wave equation with coefficients that are positive, constant outside of an interval, and have bounded variation (BV). Under the assumption of compact support of the initial data, we…
In this paper, we consider the scattering of a plane wave by a rigid obstacle embedded in a homogeneous and isotropic elastic medium in three dimensions. Based on the Helmholtz decomposition, the elastic scattering problem is reduced to a…
A theoretical scheme for the analysis of experimental data on IR spectroscopy for a quantum particle in a double well potential (DWP) is suggested. The analysis is based on the trigonometric DWP for which the exact analytic solution of the…
For the Helmholtz equation posed in the exterior of a Dirichlet obstacle, we prove that if there exists a family of quasimodes (as is the case when the exterior of the obstacle has stable trapped rays), then there exist near-zero…
We consider identical quantum bosons with weak contact interactions in a two-dimensional isotropic harmonic trap. When the interactions are turned off, the energy levels are equidistant and highly degenerate. At linear order in the coupling…
For elliptic systems with block structure in the upper half-space and t-independent coefficients, we settle the study of boundary value problems by proving compatible well-posedness of Dirichlet, regularity and Neumann problems in optimal…
For a quantum mechanical system with broken supersymmetry, we present a simple method of determining the ground state when the corresponding energy eigenvalue is sufficiently small. A concise formula is derived for the approximate ground…
The Schr\"{o}dinger equation is solved for the case of a particle confined to a small region of a box with infinite walls. If walls of the well are moved, then, due to an effective quantum nonlocal interaction with the boundary, even though…
We extend the theoretical framework of non-local optimized Schwarz methods as introduced in [Claeys,2021], considering an Helmholtz equation posed in a bounded cavity supplemented with a variety of conditions modeling material boundaries.…
Solution of Helmholtz equation with impedance boundary condition on finite interval is equivalently reformulated as steady state of initial boundary value problem for first order hyperbolic system of partial differential equations.…
We propose a novel numerical algorithm for computing the electronic structure related eigenvalue problem of incommensurate systems. Unlike the conventional practice that approximates the system by a large commensurate supercell, our…