Scattering theory

Contact:
Serge Richard (richard@math.nagoya-u.ac.jp), Rm. 237 in Sci. Bldg. A

• Description : The pdf file
  

• Schedule : Wednesday 8.45 - 10.15 in room 309 of the math building
  

• Class dates :
  April 11, 18, 25
  May 2, 9, 16, 23, 30
  June 6, 13, 20, 27
  July 4, 11, 18
  

• Program and notes taken by H. Inoue and N. Tsuzu :
  1) Hilbert space and linear operators lect. 1, lect. 2
  2) Scattering theory: time dependent approach lect. 2.5, lect. 3, lect. 4, lect. 5
  3) Scattering theory: time independent approach lect. 6, lect. 7, lect. 8
  4) Scattering theory: stationary expressions lect. 8.5, lect. 9, lect. 10, lect. 11
  5) Schroedinger operators lect. 12, lect. 13, lect. 14, lect. 15

• The cumulative notes taken by H. Inoue and N. Tsuzu, with table of content : Scattering theory

• For the evaluation, you need to submit the solutions of some exercises and/or the proofs of some statements. These submissions can take place at any time during the semester. If you have any question, contact me or Hideki Inoue

• Works submitted by the students :
  About topologies in H and in B(H), by Qiwen Sun
  About topologies in H, by Tomotaka Kunisada
  Non self-adjoint operators can have uncountable point spectrum, by Hideki Inoue
  Topologies in H and Finite rank operators, by Shuheng Liu
  Decomposition of the Hilbert space with respect to a self-adjoint operator, by Tomotaka Kunisada
  On the final range projection for the wave operators, by Ryo Hayami
  Functional calculus of unbounded operator, by Hayato Arai
  Report on Coulomb scattering, by Tomotaka Kunisada
  On the analytic Fredholm alternative and an application, by Shuheng Liu
  

• References : (electronic version available upon request)
  W. Amrein, Hilbert space methods in quantum mechanics, EPFL press, 2009.
  W. Amrein, Non-relativistic Quantum dynamics, Reidel Publishing Company, 1981.
  W. Amrein, A. Boutet de Monvel, V. Georgescu, Co-groups, commutator methods and spectral theory of N-body Hamiltonians, Birkhauser, 1996.
  H. Baumgartel, M. Wollenberg, Mathematical scattering theory, Birkhauser, 1983.
  T. Kato, Perturbation theory for linear operators, Springer, 1995.
  G. Murpy, C*-algebras and operator theory, Academic Press, 1990.
  D. Yafaev, Mathematical scattering theory: general theory, AMS, 1992.
  D. Yafaev, Mathematical scattering theory: analytic theory, AMS, 2010.