Upcoming lectures

 In the coming teaching period, I intend to present quantum mechanics for measurements with infinitely many possible outcomes. This requires two interesting tools: the spectral theorem for unbounded operators and rigged Hilbert spaces.  You are all most welcome to attend!  Probably a few QED students will attend as well.

Here is my preliminary plan:
There will be four weekly meetings of two hours on Tuesday 9.00-10.45 in the Polak building, room Y 1-23

May 8.  Spectral theorem 

  • Compact operators (section 12 Theorie spectrale (pp 62-64) from[1] and Ch 2 Review of spectral theory  and compact operators (pp 16-33) from [2] )
  • Bounded operators (Ch 3 The spectral theorem for bounded operators (pp 34-56)  from  [2])

May 15. Spectral theorem II

  • Unbounded operators (Ch 4 Unbounded operators on a Hilbert space (pp 57-78) from [2])
  • Rigged Hilbert space (Ch 29 Spectral Analysis in Rigged Hilbert Spaces (pp 439-454) from [3]; see also [4])

May 22. Quantum Mechanics for a particle on a line

  • Measurements (Ch 8 Particles and Waves (pp 235-272) from [5])
  • Between measurements (Ch 9 Particle Dynamics (pp 273-310) from [5])

June  5, 12 or 19. Harmonic Oscillator and Varia

  • Harmonic Oscillator (Ch 10 The Harmonic Oscillator (pp 311-346) from [5])
  • Spectrum (3x), Bra Ket notation, Feynman's path integral formulation

    Spectrum (3x):
    (1) p16 from [2],
    (2) page 1 of [6] theorem 10.14 of Gelfand-Mazur (p. 255) from [7],
    (3)  (Spectrum Wikipedia: `spectrum van een gloeiend gas')

    Bra Ket Notation
    This is used thoughout [5]
    Feynman's path integral formulation
    section 9,8 Path Integrals pp301-309 from [5], and  Ch 2 The Quantum-mechanical Law of Motion  (pp 25-40) from [8]

Reading material:
[1]   Michel Willem, Principes d'analyse fonctionelle (2007)
[2]  E. Kowalski, lecture notes Spectral theory in Hilbert spaces (ETH Zurich, FS 09)
 https://people.math.ethz.ch/~kowalski/spectral-theory.pdfhttps://people.math.ethz.ch/~kowalski/spectral-theory.pdf
[3] Philippe Blanchard, Erwin Bruning, Mathematical Methods in Physics (2014)
[4] Gel'fand, Vilenkin, Generalized functions volume 4.
[5] Leonard Susskind, Art Friedman, Quantum Mechanics, The Theoretical Minimum (2014)
[6] David  Mumford, The Red Book of Varieties and Schemes (1967)
[7] Walter Rudin, Functional Analysis (1991)
[8] Richard P.Feynman, Albert R.Hibbs, Quantum Mechanics and Path Integrals, Emended Edition (2010)

I hope to see you at some or all of the meetings,

J.Brinkhuis