Related papers: Solving the two dimensional Schr\"odinger equation…
The purpose of this document is to describe the solution and implementation of the time-independent and time-dependent Schr\"odinger using pseudospectral methods. Currently, the description is for single particle systems interacting with a…
The full spectrum and eigenfunctions of the quantum version of a nonlinear oscillator defined on an N-dimensional space with nonconstant curvature are rigorously found. Since the underlying curved space generates a position-dependent…
An axisymmetric space-localized solution of nonlinear electrodynamics is considered as massive charged particle with spin and magnetic moment. The appropriate solution for nonlinear electrodynamics with ring singularity is investigated. In…
We prove rigorously that the one-particle density matrix of three dimensional interacting Bose systems with a short-scale repulsive pair interaction converges to the solution of the cubic non-linear Schr\"odinger equation in a suitable…
We study a system of nonlinear Schr\"odinger equations with cubic interactions in one space dimension. The orbital stability and instability of semitrivial standing wave solutions are studied for both non-degenerate and degenerate cases.
Schr\"odinger equation belongs to the most fundamental differential equations in quantum physics. However, the exact solutions are extremely rare, and many analytical methods are applicable only to the cases with small perturbations or weak…
The standard quantum mechanics assumes Schr\"odinger equation for regular evolution and wave function collapse for measurement. As shown in this paper, only particular collapse equation can continuously transition to Schr\"odinge equation.…
A model quantum wire embedded in a matrix permeable to electron waves is investigated in terms of electronic states. The wire is assumed to have a 1D crystal structure. Through electron waves propagating in its surroundings, lateral modes…
Quantum foundations are still unsettled, with mixed effects on science and society. By now it should be possible to obtain consensus on at least one issue: Are the fundamental constituents fields or particles? As this paper shows,…
The three-dimensional Schr\"odinger equation with a position-dependent (effective) mass is studied in the framework of Supersymmetrical (SUSY) Quantum Mechanics. The general solution of SUSY intertwining relations with first order…
We study positive bound states for the semiclassical stationary nonlinear Schr\"odinger equation. We are especially interested in solutions which concentrate on a lower dimensional sphere. We adopt a purely variational approach which allows…
We revisit the treatment of identical particles in quantum mechanics. Two kinds of solutions of Schr\"{o}dinger equation are found and analyzed. First, the known symmetrized and antisymmetrized eigenfunctions. We examine how the very…
We discuss double ionization of atoms in strong laser pulses using a reduced dimensionality model. Following the insights obtained from an analysis of the classical mechanics of the process, we confine each electron to move along the lines…
The double slits experiment is a basic phenomenon, which allows to explain principal behaviour of quantum systems. However, textbooks present static pictures of corresponding interference patterns. At the same time, modern computer software…
We consider the propagation of strong gravitational waves interacting with a nonperturbative vacuum of spinor fields. To described the latter, we suggest an approximate model. The corresponding Einstein equation has the form of the…
We study the quantum dynamics of diatomic molecule driven by a circularly polarized resonant electric field. We look for a quantum effect due to classical chaos appearing due to the overlapping of nonlinear resonances associated to the…
We describe the spin and charge dynamics of the system of two electrons confined within a double quantum dot defined in a quantum wire. The spin dynamics is driven by the electron motion in presence of the spin-orbit interaction and the…
We study the two-body problem for two-dimensional electron systems in a symmetrized Bernevig-Hughes-Zhang model which is widely used to describe topological and conventional insulators. The main result is that two interacting electrons can…
A class of generalized Schr\"{o}dinger problems in bounded domain is studied. A complete overview of the set of solutions is provided, depending on the values assumed by parameters involved in the problem. In order to obtain the results, we…
We give an overview of recent advances in analysis of equations of electrodynamics with the aid of biquaternionic technique. We discuss both models with constant and variable coefficients, integral representations of solutions, a numerical…