Physics – Mathematical Physics
Scientific paper
2003-12-04
Physics
Mathematical Physics
19 pages There were made some additions (and reformulations) to the text making the derivation of the results more precise and
Scientific paper
10.1088/0305-4470/37/39/007
In present article the self-contained derivation of eigenvalue inverse problem results is given by using a discrete approximation of the Schroedinger operator on a bounded interval as a finite three-diagonal symmetric Jacobi matrix. This derivation is more correct in comparison with previous works which used only single-diagonal matrix. It is demonstrated that inverse problem procedure is nothing else than well known Gram-Schmidt orthonormalization in Euclidean space for special vectors numbered by the space coordinate index. All the results of usual inverse problem with continuous coordinate are reobtained by employing a limiting procedure, including the Goursat problem -- equation in partial derivatives for the solutions of the inversion integral equation.
Chabanov Vladimir M.
Zakhariev Boris N.
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