Báo cáo hoa học: " Research Article ¨ Some Basic Difference Equations of Schrodinger Boundary Value Problems"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article ¨ Some Basic Difference Equations of Schrodinger Boundary Value Problems | Hindawi Publishing Corporation Advances in Difference Equations Volume 2009 Article ID 569803 22 pages doi 2009 569803 Research Article Some Basic Difference Equations of Schrodinger Boundary Value Problems Andreas Ruffing 1 2 Maria Meiler 2 and Andrea Bruder3 1 Center for Applied Mathematics and Theoretical Physics CAMTP University ofMaribor Krekova Ulica 2 2000 Maribor Slovenia 2 Department of Mathematics Technische Universitat Munchen Boltzmannstrafie 3 85747 Garching Germany 3 Department of Mathematics Baylor University One Bear Place 97328 Waco TX 76798-7328 USA Correspondence should be addressed to Andreas Ruffing ruffing@ Received 1 April 2009 Accepted 28 August 2009 Recommended by Alberto Cabada We consider special basic difference equations which are related to discretizations of Schrodinger equations on time scales with special symmetry properties namely so-called basic discrete grids. These grids are of an adaptive grid type. Solving the boundary value problem of suitable Schrodinger equations on these grids leads to completely new and unexpected analytic properties of the underlying function spaces. Some of them are presented in this work. Copyright 2009 Andreas Ruffing et al. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. 1. Introduction It is well known that solving Schrodinger s equation is a prominent L2-boundary value problem. In this article we want to become familiar with some of the dynamic equations that arise in context of solving the Schrodinger equation on a suitable time scale where the expression time scale is in the context of this article related to the spatial variables. The Schrodinger equation is the partial differential equation t e R d2 d2 d2 . . d 1 -dx2 dy2 dz2 Ax y z Ax y z t i-y x-w---- i- where the function V Q c R3 R yields information on the .

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