Advertisement

Communications in Mathematical Physics

, Volume 125, Issue 2, pp 263–300 | Cite as

Inverse spectral problem for the Schrödinger equation with periodic vector potential

  • G. Eskin
Article

Abstract

For the Schrödinger operator with periodic magnetic (vector) and electric (scalar) potentials a new system of spectral invariants is found. These invariants are enough to prove the rigidity of isospectral deformations in the class of generic even and real analytic magnetic and electric potentials.

Keywords

Neural Network Statistical Physic Complex System Nonlinear Dynamics Electric Potential 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Ashcroft, N., Mermin, N. D.: Solid state physics. Philadelphia, PA,: Holt, Rinehart and Winston 1976Google Scholar
  2. 2.
    Courant, R., Hilbert, D.: Methods of mathematical physics, vol. II. New York, London: Academic Press 1962Google Scholar
  3. 3.
    Eskin, G., Ralston, J., Trubowitz, E.: On isospectral periodic potentials inR n. Commun. Pure Appl. Math.37, 647–676 (1984)Google Scholar
  4. 4.
    Eskin, G., Ralston, J., Trubowitz, E.: On isospectral periodic potentials inR n, II. Commun. Pure Appl. Math.37, 715–753 (1984)Google Scholar
  5. 5.
    Guillemin, V., Uribe, A.: Clustering theorems with twisted spectra. Math. Ann.2731, 479–506 (1986)Google Scholar
  6. 6.
    Maslov, V. P., Fedoriuk, M. V.: Semi-classical approximation in quantum mechanics. Dordrecht: D. Reidel 1981Google Scholar

Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • G. Eskin
    • 1
  1. 1.Department of MathematicsUniversity of CaliforniaLos AngelesUSA

Personalised recommendations