相关论文: On a general solution of the one-dimensional stati…

A slightly modified variant of the cubic periodic one-dimensional nonlinear Schroedinger equation is shown to admit weak solutions for all initial data in certain function spaces wider than L^2. These solutions depend uniformly continuously…

We present analytic formulae that simplify the evaluation of the normalization of continuous spectrum stationary states in the one-dimensional Schr\"odinger equation.

Necessary and sufficient conditions for existence of boundary value problem of Schrodinger equation are obtained in linear and nonlinear cases. Periodic analytical solutions are represented using generalized Green's operator

We review an exact WKB resolution method for the stationary 1D Schr\"odinger equation with a general polynomial potential. This contribution covers already published material: we supply a commented summary here, stressing a few aspects…

All stationary solutions to the one-dimensional nonlinear Schroedinger equation under box and periodic boundary conditions are presented in analytic form. We consider the case of repulsive nonlinearity; in a companion paper we treat the…

We discuss the explicit construction of the Schroedinger equations admitting a representation through some family of general polynomials. Almost all solvable quantum potentials are shown to be generated by this approach. Some generalization…

We obtain a complete series solution of stationary Schr\"odinger's equation in the general quantum systems. It is exact in the sense that any approximation means is not used, or that the whole corrections or contributions from all order…

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…

The Schrodinger equation for stationary states is studied in a central potential V(r) proportional to the inverse power of r of degree beta in an arbitrary number of spatial dimensions. The presence of a single term in the potential makes…

This work presents a direct and highly accurate method to solve ordinary differential equations, in particular the Schr\"odinger equation in one dimension, through the direct substitution of a power series solution to obtain a purely…

A method is given to construct globally analytic (in space and time) exact solutions to the focusing cubic nonlinear Schrodinger equation on the line. An explicit formula and its equivalents are presented to express such exact solutions in…

The analytical solutions of the N-dimensional Schrodinger equation with position-dependent mass for a general class of central potentials is obtained via the series expansion method. The position-dependent mass is expanded in series about…

The goal is a construction of stationary solutions close to a non-trivial combination of two plane waves at high energies for a periodic non-linear Schroedinger equation in dimension two. The corresponding isoenergetic surfaces are…

Evaluation of a product integral with values in the Lie group SU(1,1) yields the explicit solution to the impedance form of the Schr\"odinger equation. Explicit formulas for the transmission coefficient and $S$-matrix of the classical…

The wave equation in quantum mechanics and its general solution in the phase space are obtained.

The energy-based stochastic extension of the Schrodinger equation is a rather special nonlinear stochastic differential equation on Hilbert space, involving a single free parameter, that has been shown to be very useful for modelling the…

It is shown that using the similarity transformations, a set of three-dimensional p-q nonlinear Schrodinger (NLS) equations with inhomogeneous coefficients can be reduced to one-dimensional stationary NLS equation with constant or varying…

In this paper we consider stationary solutions to the nonlinear one-dimensional Schroedinger equation with a periodic potential and a Stark-type perturbation. In the limit of large periodic potential the Stark-Wannier ladders of the linear…

We present basic results, known and new, on nontrivial solutions of periodic stationary nonlinear Schr\"odinger equations. We also sketch an application to nonlinear optics and discuss some open problems.

Given a first-order autonomous algebraic ordinary differential equation, we present a method for computing formal power series solutions by means of places. We provide an algorithm for computing a full characterization of possible initial…