One Dimensional Schrödinger Equation With Two Moving Boundaries
نویسنده
چکیده
In this letter, we consider the Schrödinger equation for a well potential with varying width. We solve one dimensional Schrödinger equation subject to time-dependent boundary conditions for a spinless particle inside infinite potential well, both wall of which move opposite direction with different velocities υ1 and υ2, respectively. PACS numbers: 03.65.Ge Typeset using REVTEX
منابع مشابه
Localized Nonlinear Waves in Nonlinear Schrödinger Equation with Nonlinearities Modulated in Space and Time
In this paper, the generalized sub-equation method is extended to investigate localized nonlinear waves of the one-dimensional nonlinear Schrödinger equation (NLSE) with potentials and nonlinearities depending on time and on spatial coordinates. With the help of symbolic computation, three families of analytical solutions of this NLS-type equation are presented. Based on these solutions, period...
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 کاملExact Moving Breather Solutions of a Generalized Discrete Nonlinear Schrödinger Equation
We obtain exact moving breather solutions of a generalized discrete nonlinear Schrödinger equation. For finite lattices, we find two different moving periodic breather solutions while for an infinite lattice we find a localized moving breather solution.
متن کاملAbsorbing Boundary Conditions for the Two-Dimensional Schrödinger Equation with an Exterior Potential. Part I: Construction and a priori Estimates
The aim of this paper is to construct some classes of absorbing boundary conditions for the two-dimensional Schrödinger equation with a time and space varying exterior potential and for general convex smooth boundaries. The construction is based on asymptotics of the inhomogeneous pseudodifferential operators defining the related Dirichlet-to-Neumann operator. Furthermore, a priori estimates ar...
متن کاملWhen the classical & quantum mechanical considerations hint to a single point; a microscopic particle in a one dimensional box with two infinite walls and a linear potential inside it
In this paper we have solved analytically the Schrödinger equation for a microscopic particle in a one-dimensional box with two infinite walls, which the potential function inside it, has a linear form. Based on the solutions of this special quantum mechanical system, we have shown that as the quantum number approaches infinity the expectation values of microscopic particle position and square ...
متن کامل