Publications of the Scuola Normale Superiore

Integrable Hamiltonian systems and spectral theory

Authors: Moser, Jürgen

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About this book

These notes are based on six Fermi Lectures held at the Scuola Normale Superiore in Pisa in March and April 1981. The topics treated depend on basic concepts of classical mechanics, elementary geometry, complex analysis as well as spectral theory and are meant for mathematicians and theoretical physicists alike. These lectures weave together a number of threads from various fields of mathematics impinging on the subject of inverse spectral theory. I did not try to give an overview over this fast moving subject but rather tie various aspects together by one guiding theme: the construction of all potentials for the one-dimensional Schrödinger equation which gives rise to finite band potentials, which is done by reducing it to solving a system of differential equations. In fact, we will see that the problem of finding all almost periodic potentials having finitely many intervals as its spectrum is equivalent to the study of the geodesics on an ellipsoid. To make this connection clear we have carried together several facts from classical mechanics and from spectral theory and we give a self-contained exposition of the construction of these finite band potentials.

Buy this book

Softcover $24.95 net
( price for USA )
  • ISBN 978-88-7642-252-2
  • free shipping for individuals worldwide
  • online orders shipping within 2-3 days.

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Bibliographic Information

Bibliographic Information
Book Title
Integrable Hamiltonian systems and spectral theory
Series Title
Publications of the Scuola Normale Superiore
Copyright
1983
Publisher
Edizioni della Normale
Copyright Holder
Edizioni della Normale
Softcover ISBN
978-88-7642-252-2
Edition Number
1
Topics