Modal expansions and completeness relations for some time-dependent Schrödinger equations
نویسندگان
چکیده
With the use of a variant of the method of separation of variables, the initial value problem for the time-dependent linear Schrödinger equation is solved exactly for a large class of potential functions related to multisoliton interactions in the vector nonlinear Schrödinger equation. Completeness of states is proved for absolutely continuous initial data in L1. Copyright © 1998 Elsevier Science B.V. PACS: 02.30.Jr; 03.40.Kf; 03.65.Ge
منابع مشابه
Eigenfunction Expansions for Second-Order Boundary Value Problems with Separated Boundary Conditions
In this paper, we investigate some properties of eigenvalues and eigenfunctions of boundary value problems with separated boundary conditions. Also, we obtain formal series solutions for some partial differential equations associated with the second order differential equation, and study necessary and sufficient conditions for the negative and positive eigenvalues of the boundary value problem....
متن کاملFlow-Induced Instability Smart Control of Elastically Coupled Double-Nanotube-Systems
Flow induced vibration and smart control of elastically coupled double-nanotube-systems (CDNTSs) are investigated based on Eringen’s nonlocal elasticity theory and Euler-Bernoulli beam model. The CDNTS is considered to be composed of Carbon Nanotube (CNT) and Boron-Nitride Nanotube (BNNT) which are attached by Pasternak media. The BNNT is subjected to an applied voltage in the axial direction w...
متن کاملAixsymmetric Stagnation Point Flow of a Viscous Fluid on a Moving Cylinder with Time Dependent Axial Velocity
The unsteady viscous flow in the vicinity of an axisymmetric stagnation point of an infinite moving cylinder with time-dependent axial velocity is investigated. The impinging free stream is steady with a strain rate k. An exact solution of the Navier-Stokes equations is derived in this problem. A reduction of these equations is obtained by use of appropriate transformations. The general self-si...
متن کاملOn completeness results for predicate
In this paper we deal with generic expansions of first-order predicate logics of some left-continuous t-norms with a countable set of truth-constants. Besides already known results for the case of Lukasiewicz logic, we obtain new conservativeness and completenesss results for some other expansions. Namely, we prove that the expansions of predicate Product, Gödel and Nilpotent Minimum logics wit...
متن کاملCompleteness-via-canonicity for coalgebraic logics
This thesis aims to provide a suite of techniques to generate completeness results for coalgebraic logics with axioms of arbitrary rank. We have chosen to investigate the possibility to generalize what is arguably one of the most successful methods to prove completeness results in ‘classical’ modal logic, namely completeness-via-canonicity. This technique is particularly well-suited to a coalge...
متن کامل