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19th GAMM-Seminar Leipzig on
High-dimensional problems - Numerical treatment and applications

Max-Planck-Institute for Mathematics in the Sciences
Inselstr. 22-26, D-04103 [O->]Leipzig
Phone: +49.341.9959.752, Fax: +49.341.9959.999


     
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  19th GAMM-Seminar
January, 23th-25th, 2003
 
     
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  Abstract Hermann Render, Thu, 18.00-18.25 Previous Contents Next  
  A model for the Schrödinger operator
Hermann Render (Gerhard-Mercator Universität Duisburg)

Discretizations of the Schrödinger Operator in the one-dimensional case, i.e. of the Sturm-Liouville Operator, can be analysed by means of orthogonal polynomials.

Further, by the theorem of M. Stone, these operators are unitarily equivalent to a multiplication operator with a variable x on a Hilbert space tex2html_wrap_inline14 where tex2html_wrap_inline16 is the spectral measure of the operator.

In this talk, which is based on joint work with O. Kounchev (Bulgarian Academy of Sciences), we want to discuss representations of the Schrödinger Operator as multiplication with tex2html_wrap_inline18 on a Hilbert space tex2html_wrap_inline20, where tex2html_wrap_inline22 is a suitable non-negative measure over tex2html_wrap_inline24 and tex2html_wrap_inline26 is the euclidean norm.

Special attention is devoted to semi-discretizations of the Schrödinger operator on the strip and an explicit solution for the problem is given for the case of separable potentials.
 

 
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