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Semiclassical theory of shape resonances in quantum mechanics

About this Title

P. D. Hislop and I. M. Sigal

Publication: Memoirs of the American Mathematical Society
Publication Year: 1989; Volume 78, Number 399
ISBNs: 978-0-8218-2462-7 (print); 978-1-4704-0819-0 (online)
DOI: https://doi.org/10.1090/memo/0399
MathSciNet review: 989524
MSC: Primary 81C15; Secondary 35J10, 47F05

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Table of Contents

Chapters

  • 1. Introduction
  • 2. The model and the approximate Hamiltonian
  • 3. Preliminaries: The spectra of $H_0(\lambda )$ and $H(\lambda )$
  • 4. The distorted Hamiltonians
  • 5. Harmonic approximation
  • 6. Existence of resonances
  • 7. Exponential decay of eigenfunctions
  • 8. Width of the resonances
  • 9. Comments
  • 10. Appendix A. Proof of Theorem 6.2
  • 11. Appendix B. Uniform boundedness of the resolvent of the reduced Hamiltonian
  • Supplement. The spectra of the distorted Hamiltonians