Miscellaneous Approaches to the Inverse Problems at Fixed l
This chapter is a survey of further generalizations of the methods which have been described in previous chapters, new approaches, and approaches to more complicated problems. The study is limited to radial problems (for “one dimensional” problems see Chapter XVII). Throughout this chapter, most results are stated without proof and the reader who is interested in these proofs should refer to the literature. The notations are either the ones that are used elsewhere in this book or are specially given in each section.
KeywordsInverse Problem Dispersion Relation Spectral Function Regular Solution Schrodinger Equation
Unable to display preview. Download preview PDF.
- Blazek M. (1962b): Explicit determination of a potential with n bound states by means of the solution of the inverse problem, Czech. J. Phys. B12, 258–263 (sections IV.H, IX.9, Foreword) Google Scholar
- Chadan K., and Montes A. (1968): Derivation of nonrelativistic sum rules from the causality condition of Wigner and Van Kampen, J. Math. Phys. 9, 1898–1914 (sections V.H, IX.9)Google Scholar
- Cornille H. (1967): Connection between the Marchenko formalism and N/D equations: Regular interactions I. J. Math. Phys. 8, 11, 2268–2281 (section VII.H)Google Scholar
- Dyson F. J. (1976a): Old and new approaches to the inverse scattering problem in Studies in Mathematical Physics, ed. by E. H. Lieb, B. Simon, and A. S. Wightman, PrincetonGoogle Scholar
- Glaser V., Martin A., Grosse H., and Thirring W. (1976): A family of optimal conditions for the absence of bound states in a potential: in Studies in Mathematical Physics, edited by E. H. Lieb, B. Simon, and A. S. Wightman, PrincetonGoogle Scholar
- Martin A., and Sabatier P. C. (1977): Impedance, zero energy wave-function, and bound states. To be published in J. Math. Phys. (section 1X. 9 )Google Scholar
- Sabatier P. C. (1974a): Construction of the scattering amplitude from the elastic cross section at a given energy, Invited lecture in the Summer School on Inverse problems organized by the American Mathematical Society in Los Angeles. Cahiers mathématiques de Montpellier, 4 (section X.1, Foreword)Google Scholar
- Sabatier P. C. (1974b): Problème direct et inverse de diffraction d’une onde élastique par une zone perturbée sphérique, C. R. Acad. Sci. Paris 278, série B, 545–547 section VI.H, Foreword)Google Scholar
- Sabatier P. C. (1977): On geophysical inverse problems and constraints, J. Geophys. 43, 115–137.Google Scholar