Spectral and scattering inverse problems

Journal Article · Fri Dec 01 04:00:00 EST 1978 · J. Math. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1063/1.523645· OSTI ID:6919144

Sabatier, P C

The reconstruction of a differential operator form discrete spectra is reduced to its reconstruction from an S-matrix. This method makes it possible to solve the singular Sturm--Liouville problems which determine certain modes of a sphere. The results pave the way for handling studies in which information on modes and scattering results would all be taken into account. They are applied to the earth inverse problem and partial answers are given to a well-known conjecture. Finally the relevance of the JWKB approximation in this kind of problem is briefly discussed.

• Research Organization: Laboratoire de Physique Mathematique, Universite des Sciences et Techniques du Languedoc, 34060 Montpellier Cedex, France
• OSTI ID: 6919144
• Journal Information: J. Math. Phys. (N.Y.); (United States), Journal Name: J. Math. Phys. (N.Y.); (United States) Vol. 19:12; ISSN JMAPA
• Country of Publication: United States
• Language: English

Related Subjects

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658000 -- Mathematical Physics-- (-1987)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ASYMPTOTIC SOLUTIONS
DIFFERENTIAL EQUATIONS
EQUATIONS
INVERSE SCATTERING PROBLEM
MATRICES
S MATRIX
SINGULARITY
SPECTRA
STURM-LIOUVILLE EQUATION