相关论文: Wavelet basis for the Schr\"{o}dinger equation

It is shown that the Schr\"{o}dinger equation for a system of interacting particles whose Compton wavelengths are of the same order of magnitude as the system size is contradictory and is not strictly nonrelativistic, because it is based on…

This paper can be considered as a sequel of [BS14] by Bernicot and Samoyeau, where the authors have proposed a general way of deriving Strichartz estimates for the Schr{\"o}dinger equation from a dispersive property of the wave propagator.…

Schrodinger's equation for a single particle is proved from the assumption that dynamics can be formulated in a space whose curvature is the electromagnetic force.

This paper proves existence and stability results of solitary-wave solutions to coupled nonlinear Schr\"{o}dinger equations with power-type nonlinearities arising in several models of modern physics. The existence of solitary waves is…

The Schr\"{o}dinger equation, in hyperspherical coordinates, is solved in closed form for a system of three particles on a line, interacting via pair delta functions. This is for the case of equal masses and potential strengths. The…

The present paper is the first part of a project devoted to the fractional nonlinear Schr\"{o}dinger (fNLS) equation. It is concerned with the existence and numerical generation of the solitary-wave solutions. For the first point, some…

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…

The wave equation on a bounded domain of $\R^{n}$ with non homogeneous boundary Dirichlet data or sources supported on a subset of the boundary is considered. We analyze the problem of observing the source out of boundary measurements done…

We present the random behaviour of the Schr\"odinger map equation, a geometric partial differential equation, by considering its evolution for regular polygonal curves in both Euclidean and hyperbolic spaces. The results obtained are…

A principle is proposed according to which the dynamics of a quantum particle in a one-dimensional configuration space (OCS) is determined by a variational problem for two functionals: one is based on the mean value of the Hamilton…

We formulate the Schr\"odinger equation as the equation of motion of a small external influence which serves as the initial boundary condition of a physical system in classical laboratory space. The Hilbert space of possible external…

The connection between derivative operators and wavelets is well known. Here we generalize the concept by constructing multiresolution approximations and wavelet basis functions that act like Fourier multiplier operators. This construction…

The eigenvalues and a series representation of the eigenfunctions of the Schrodinger equation for a particle on the surface of a torus are derived.

Exact expressions are obtained for a diversity of propagating patterns for a derivative nonlinear Schr\"odinger equation with a quintic nonlinearity. These patterns include bright pulses, fronts and dark solitons. The evolution of the wave…

Sea ice attenuates waves propagating from the open ocean. Here we model the evolution of energetic unidirectional random waves in the marginal ice zone with a nonlinear Schr\"{o}dinger equation, with a frequency dependent dissipative term…

We describe a certain "self-similar" family of solutions to the free Schroedinger equation in all dimensions, and derive some consequences of such solutions for two specific problems.

This paper is concerned with the derivative nonlinear Schr\"{o}dinger equation with periodic boundary conditions. We obtain complete Birkhoff normal form of order six. As an application, the long time stability for solutions of small…

The Wheeler - DeWitt geometrodynamics, as the first attempt to develop a quantum theory of gravity, faces certain challenges, including the problem of time and the interpretation of the wave function. In this paper, we present the extended…

Due to the space and time dependence of the wave function in the time dependent Schroedinger equation, different boundary conditions are possible. The equation is usually solved as an ``initial value problem'', by fixing the value of the…

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…