Accession Number : AD0657566

Title :   CONSTRUCTION OF EIGENFUNCTION EXPANSIONS BY THE PERTURBATION METHOD AND ITS APPLICATION TO N-DIMENSIONAL SCHRODINGER OPERATIONS.

Descriptive Note : Technical summary rept.,

Corporate Author : WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER

Personal Author(s) : Kuroda,S. T.

Report Date : MAY 1967

Pagination or Media Count : 61

Abstract : An operator-theoretical approach to the construction of eigenfunction expansions by the perturbation method is discussed. Eigenfunction expansions in this paper mean those associated with continuous spectra. The method is to combine a stationary approach to the scattering theory with the now well developed idea of formulating generalized eigenfunction expansions in terms of a triplet of spaces. Given an expansion associated with the unperturbed operator, two complete sets of eigenfunctions of the perturbed operator are constructed and shown to be the unique solution of the Lippmann-Schwinger equation in a modified form. As an application, spectral properties of the n-dimensional Schrodinger operator -delta + f(x) are investigated in detail.

Descriptors :   (*FUNCTIONS(MATHEMATICS), PERTURBATION THEORY), (*OPERATORS(MATHEMATICS), QUANTUM THEORY), SCATTERING, MAPPING(TRANSFORMATIONS), HILBERT SPACE, INEQUALITIES, THEOREMS

Subject Categories : Theoretical Mathematics
      Quantum Theory and Relativity

Distribution Statement : APPROVED FOR PUBLIC RELEASE