On Time-Splitting Spectral Approximationsfor the Schrodinger Equation in theSemiclassical Regime
نویسندگان
چکیده
On Time-Splitting Spectral Approximations for the Schrödinger Equation in the Semiclassical Regime Weizhu Bao,∗ Shi Jin,† and Peter A. Markowich‡ ∗Department of Computational Science, National University of Singapore, Singapore 117543; †Department of Mathematics, University of Wisconsin-Madison, Madison, Wisconsin 53706; and ‡Institute of Mathematics, University of Vienna Boltzmanngasse 9, A-1090 Vienna, Austria E-mail: [email protected]; [email protected]; [email protected].
منابع مشابه
Inverse scattering problem for the Impulsive Schrodinger equation with a polynomial spectral dependence in the potential
In the present work, under some di¤erentiability conditions on the potential functions , we rst reduce the inverse scattering problem (ISP) for the polynomial pencil of the Scroedinger equation to the corresponding ISP for the generalized matrix Scrödinger equation . Then ISP will be solved in analogy of the Marchenko method. We aim to establish an e¤ective algorithm for uniquely reconstructin...
متن کاملThe smoothed particle hydrodynamics method for solving generalized variable coefficient Schrodinger equation and Schrodinger-Boussinesq system
A meshless numerical technique is proposed for solving the generalized variable coefficient Schrodinger equation and Schrodinger-Boussinesq system with electromagnetic fields. The employed meshless technique is based on a generalized smoothed particle hydrodynamics (SPH) approach. The spatial direction has been discretized with the generalized SPH technique. Thus, we obtain a system of ordinary...
متن کاملOn the Time Splitting Spectral Method for the Complex Ginzburg-Landau Equation in the Large Time and Space Scale Limit
We are interested in the numerical approximation of the complex Ginzburg–Landau equation in the large time and space limit. There are two interesting regimes in this problem, one being the large space time limit, and one being the nonlinear Schrodinger limit. These limits have been studied analytically in, for example, [7, 18, 19]. We study a time splitting spectral method for this problem. In ...
متن کاملSymplectic splitting operator methods for the time-dependent Schrodinger equation.
We present a family of symplectic splitting methods especially tailored to solve numerically the time-dependent Schrodinger equation. When discretized in time, this equation can be recast in the form of a classical Hamiltonian system with a Hamiltonian function corresponding to a generalized high-dimensional separable harmonic oscillator. The structure of the system allows us to build highly ef...
متن کاملOn the Numerical Solution of One Dimensional Schrodinger Equation with Boundary Conditions Involving Fractional Differential Operators
In this paper we study of collocation method with Radial Basis Function to solve one dimensional time dependent Schrodinger equation in an unbounded domain. To this end, we introduce artificial boundaries and reduce the original problem to an initial boundary value problem in a bounded domain with transparent boundary conditions that involves half order fractional derivative in t. Then in three...
متن کامل