Rocky Mountain Mathematical Physics Seminar

Content: The goal of this semester (Spring 2026) is to study the
Mathematics of Schrödinger operators and applications in quantum many-body theory and quantum chemistry..
Organizer: Markus Pflaum and Gregory Berkolaiko,
Hours and Venue: Wednesday 2:10 p.m. - 3:00 p.m., MATH 350
Online Option: Meeting ID: 970 4917 3677 (for the Passcode please contact the organizers)
Topics and talks:
  • Introduction to Schrödinger operators and organizational meeting (Markus Pflaum, Feb 4)
  • Warm-up: Visualizing Schrödinger's equation in finite dimensions (Gregory Berkolaiko, Feb 11)
    Abstract: As a warm-up for the semester, we will explore the time evolution in a finite-dimensional (d=2 mostly) Schrödinger equation, its relation to the quadratic form and their visualization on the Bloch sphere. If time permits, we will briefly discuss why a 2-dimensional picture is sometimes appropriate even when working with unbounded Schrödinger operators.
  • The spectral theorem and projection valued measures I (Howy Jordan, Feb 18)
  • The spectral theorem and projection valued measures II (Howy Jordan, Feb 25)
  • Mathematical approaches to chemical bond according to Heitler-London and Hückl (Markus Pflaum, March 4)
  • Periodic Schrödinger operators and Bloch theory I (Evan Wickenden, March 25)
  • Periodic Schrödinger operators and Bloch theory II (Evan Wickenden, April 1)
  • Kato's theorem on the selfadjointness of the molecular Hamiltonian (Scott Maccarone, April 8)
  • The Bargmann-Segal representation and Schrödinger operators (Saksham Hassanandani, April 15)
  • Mudassir Moosa, TBA, April 22
  • The Born-Oppenheimer approximation ()
  • The potential energy surface of a molecule ()
  • Hartree-Fock Molecular Orbital Theory ()
  • Conical intersections ()
  • Geometric Quantum Mechanics ()
Literature:
  • Online Resources on mathematical foundations and geometric quantum mechanics:

    • Pflaum, M.J. et al., The FANCy Project on Functional Analysis and Noncommutative Geometry.

    Takhtajan, L.A., Quantum Mechanics for Mathematicians, AMS (2008).