Related papers: Bound states and the potential parameter spectrum
We consider the radial Schr\" odinger equation with the pseudo-Gaussian potential. By making an ansatz to the solution of the eigenvalue equation for the associate Hamiltonian, we arrive at the general exact eigenfunction. The values of…
We describe a non-perturbative method for computing the energy band structures of one-dimensional models with general point potentials sitting at equally spaced sites. This is done thanks to a Bethe ansatz approach and the method is…
We consider the focusing energy-critical nonlinear wave equation for radially symmetric initial data in space dimensions $D \ge 4$. This equation has a unique (up to sign and scale) nontrivial, finite energy stationary solution $W$, called…
An explicit expression for the finite-volume energy shift of shallow three-body bound states for non-identical particles is obtained in the unitary limit. The inclusion of the higher partial waves is considered. To this end, the method of…
On the contrary to the common intuition, which suggests that a steep expulsive potential makes quantum states widely delocalized, we demonstrate that one- and two-dimensional (1D and 2D) Schroedinger equations, which include expulsive…
In this paper we discuss energy conservation issues related to the numerical solution of the nonlinear wave equation. As is well known, this problem can be cast as a Hamiltonian system that may be autonomous or not, depending on the…
The finite square potential well is a staple problem in introductory quantum mechanics. There is an extensive literature on the determination of the allowed energies, which requires the solution of a transcendental equation by numerical,…
Large-time asymptotic properties of solutions to a class of semilinear stochastic wave equations with damping in a bounded domain are considered. First an energy inequality and the exponential bound for a linear stochastic equation are…
We study rotating wave solutions of the nonlinear wave equation $$ \left\{ \begin{aligned} \partial_{t}^2 v - \Delta v + m v & = |v|^{p-2} v \quad && \text{in $\mathbb{R} \times \mathbf{B}$} \\ v & = 0 && \text{on $\mathbb{R} \times…
The equation is considered for a composite scalar particle with polarizabilities in an external quantized electromagnetic plane wave. This equation is reduced to a system of equations for infinite number of interacting oscillators. After…
In the paper the Schr\"odinger equation for quasibound resonance state with complex energy is considered. The system of inhomogeneous differential equations is obtained for the real and imaginary parts of wave function. On the base of known…
The spectrum of a bound state of three identical particles with a mass $m$ in a finite cubic box is studied. It is shown that in the unitary limit, the energy shift of a shallow bound state is given by $\Delta E=c (\kappa^2/m)\,(\kappa…
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…
In this paper, we continue our study [16] on the long time dynamics of radial solutions to defocusing energy critical wave equation with a trapping radial potential in 3 + 1 dimensions. For generic radial potentials (in the topological…
The Faddeev equations for the three body bound state are solved directly as three dimensional integral equation without employing partial wave decomposition. The numerical stability of the algorithm is demonstrated. The three body binding…
An alternative approximation scheme has been used in solving the Schrodinger equation for the exponential-cosine-screened Coulomb potential. The bound state energ\i es for various eigenstates and the corresponding wave functions are…
We study the inverse boundary value problem for the wave equation using the single-layer potential operator as the data. We assume that the data have frequency content in a bounded interval. We prove how to choose classes of nonsmooth…
This article addresses the inverse problem of simultaneously recovering both the wave speed coefficient and an unknown initial condition (acting as the source) for the multidimensional wave equation from a single passive boundary…
At the lower edge of the energy continuum the birth of an isolated quantum bound state is studied as caused by an infinitesimally small change of the interaction. In our model a single, asymptotically free massive quantum particle is…
We consider a system of three particles, either three identical bosons or two identical fermions plus an impurity, within a three-dimensional isotropic trap interacting via a contact interaction. Using two approaches, one using an infinite…