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On the Cauchy Problem for the Schrödinger Equation with Generator of Variable Type

On the Cauchy Problem for the Schrödinger Equation with Generator of Variable Type Differential Equations, Vol. 40, No. 2, 2004, pp. 241–255. Translated from Differentsial'nye Uravneniya, Vol. 40, No. 2, 2004, pp. 229–241. Original Russian Text Copyright c 2004 by Sakbaev. PARTIAL DIFFERENTIAL EQUATIONS On the Cauchy Problem for the Schr odinger Equation with Generator of Variable Type V. Zh. Sakbaev Moscow Institute of Physics and Technology, Moscow, Russia Received November 16, 2001 1. INTRODUCTION In a number of problems of nonlinear optics, solid-state physics, and plasma physics, one has to deal with the motion of mechanical systems with variable e ective mass [1]. If the e ective mass of a system vanishes at some points of the coordinate space (or the phase space), then the description of the dynamics of the mechanical system by equations of classical mechanics becomes nonunique [1, 2]. In the present paper, we make an attempt to describe the motion of such systems with the use of equations of quantum mechanics. We study the well-posedness of the Cauchy problem for the Schr odinger equation whose Hamil- tonian is a di erential operator of variable type: @u(t;x) i = Lu(t;x);t> 0;x 2 R;n 2 N: (1) @t Equation (1) is supplemented by the initial condition u(+0;x)= u (x): http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Differential Equations Springer Journals

On the Cauchy Problem for the Schrödinger Equation with Generator of Variable Type

Sakbaev, V.
Differential Equations , Volume 40 (2) – Oct 18, 2004
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References (3)

Publisher
Springer Journals
Copyright
Copyright © 2004 by MAIK “Nauka/Interperiodica”
Subject
Mathematics; Difference and Functional Equations; Ordinary Differential Equations; Partial Differential Equations
ISSN
0012-2661
eISSN
1608-3083
DOI
10.1023/B:DIEQ.0000033713.50221.81
Publisher site
See Article on Publisher Site

Abstract

Differential Equations, Vol. 40, No. 2, 2004, pp. 241–255. Translated from Differentsial'nye Uravneniya, Vol. 40, No. 2, 2004, pp. 229–241. Original Russian Text Copyright c 2004 by Sakbaev. PARTIAL DIFFERENTIAL EQUATIONS On the Cauchy Problem for the Schr odinger Equation with Generator of Variable Type V. Zh. Sakbaev Moscow Institute of Physics and Technology, Moscow, Russia Received November 16, 2001 1. INTRODUCTION In a number of problems of nonlinear optics, solid-state physics, and plasma physics, one has to deal with the motion of mechanical systems with variable e ective mass [1]. If the e ective mass of a system vanishes at some points of the coordinate space (or the phase space), then the description of the dynamics of the mechanical system by equations of classical mechanics becomes nonunique [1, 2]. In the present paper, we make an attempt to describe the motion of such systems with the use of equations of quantum mechanics. We study the well-posedness of the Cauchy problem for the Schr odinger equation whose Hamil- tonian is a di erential operator of variable type: @u(t;x) i = Lu(t;x);t> 0;x 2 R;n 2 N: (1) @t Equation (1) is supplemented by the initial condition u(+0;x)= u (x):

Journal

Differential Equations – Springer Journals

Published: Oct 18, 2004

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