Hilbert space methods for quantum mechanics

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 13, 20, 27
  May 11, 18, 25
  June 1, 8, 15, 22, 29
  July 6, 13, 20
  

• Lecture notes : full document, 100 pages
  Hilbert space methods for quantum mechanics
  

• Lecture notes :
  Title
  Contents
  Chapter 1: Hilbert space and bounded linear operators
  Chapter 2: Unbounded operators
  Chapter 3: Examples
  Chapter 4: Spectral theory for self-adjoint operators
  Chapter 5: Scattering theory
  Chapter 6: Commutator methods
  Bibliography
  

• Student reports :
  On multiplication operator by Keigo Shibuya
  Wigner-Bargmann's theorem by Keigo Shibuya
  Hilbert Schmidt operators by Yukino Takeuchi
  Reflexive space and relation between norm and inner product by Yuki Demachi
  Equalities of equivalence relations by Ippei Mimura
  On a density property in Sobolev spaces by Takashi Furuya
  Investigation of the hydrogen atom by Son Nguyen
  Beautiful oral presentations of this paper by Hideki Inoue
  On the spectral theorem by Kenta Oishi
  

• References : (electronic version available upon request)
  [Amr] W. Amrein, Hilbert space methods in quantum mechanics, Fundamental Sciences. EPFL Press, Lausanne 2009.
  [ABG] W. Amrein, A. Boutet de Monvel, V. Georgescu, Co-groups, commutator methods and spectral theory of N-body Hamiltonians Birkhäuser, Basel, 1996.
  [BW] H. Baumgartel, M. Wollenberg, Mathematical scattering theory, Birkhäuser verlag, Basel, 1983.
  [BDG] L. Bruneau, J. Derezinski, and V. Georgescu, Homogeneous Schroedinger operators on half-line, Ann. Henri Poincare 12 no. 3 (2011), 547 - 590.
  [DR] J. Derezinski, and S. Richard, On almost homogeneous Schroedinger operators, Preprint arXiv:1604.03340.
  [Hal] B. Hall, Quantum theory for mathematicians, Graduate Texts in Mathematics 267. Springer, New York, 2013.
  [Kat] T. Kato, Perturbation theory for linear operators, Classics in mathematics, Springer, 1995.
  [Mur] G.J. Murphy, C*-algebras and operator theory Academic Press, Inc., Boston, MA, 1990.
  [Ped] G. Pedersen, Analysis now Graduate texts in mathematics 118, Springer, 1989.
  [RS3] M. Reed and B. Simon, Methods of modern mathematical physics III: scattering theory, Academic Press, Inc., 1979.
  [RS4] M. Reed and B. Simon, Methods of modern mathematical physics IV: analysis of operators, Academic Press, Inc., 1978.
  [Ric] S. Richard, Levinson's theorem: an index theorem in scattering theory, in Operator Theory Advances and Applications 254, 149 – 203, Birkhäuser, 2016.
  [Tes] G. Teschl, Mathematical methods in quantum mechanics, with applications to Schrödinger operators, Graduate Studies in Mathematics 99. American Mathematical Society, Providence, RI, 2009.
  [Yaf] D.R. Yafaev, Mathematical scattering theory. General theory, Translations of Mathematical Monographs 105, American Mathematical Society, Providence, RI, 1992.