Mathematical Foundations of Modern Quantum Many-Body Theory
Rensselaer Polytechnic Institute MATH 6940, Spring 2024
This is the official website for the reading course: Mathematical Foundations of Modern Quantum Many-Body Theory, held in Spring 2024
General information
Instructor: Fabian M. Faulstich
Time: Tue 4:00PM - 6:00PM Amos Eaton 411
Office Hours: Tue 1:00PM-2:00PM, Thu 4:00PM-5PM. 406 Amos Eaton Hall
Schedule
| Date | Topic | Presenter |
|---|---|---|
| 01/10 | Overview of the Quantum Many-Body Problem | Fabian Faulstich |
| 01/16 | Quantum mechanics of the hydrogen atom | Timothy Lund |
| 01/23 | The hydrogen molecule and the Hartree-Fock method | Ben Freiman |
| 01/30 | Second quantization I: Fock space, creation and annihiliation operators, Excitation operators | Michael Papadopoulos |
| 02/06 | No meeting | |
| 02/13 | No meeting | |
| 02/20 | Recap: the Hartree-Fock method (first quantization) | Fabian Faulstich |
| 02/27 | No meeting | |
| 03/12* | Second quantization II: Slater-Condon rules, Wick's theorem, Hartree-Fock revisited | Edward Lu |
| 03/19 | No meeting | |
| 03/26* | The linear combination of atomic orbitals ansatz | Chanaka Mapa Mudiyanselage |
| 04/02 | Gaussian-type atomic orbitals and high-dimensional integration | Talha Aziz |
| 04/09 | Truncating the coupled cluster ansatz and its working equations | Ibrahim Abdulazeez |
| 04/16 | Finding one and all roots to the coupled cluster equations | Francis Appiah |
Meetings marked with an asterisk (*) are subject to potential cancellation. In case this happens, the scheduled presenter for that date will present at the next occurring meeting, causing all subsequent presenters to be rescheduled to the following occuring dates.
Textbooks
Mathematics:
A Mathematical Introduction To Electronic Structure Theory by Lin Lin and Jianfeng LuChemistry:
Molecular Electronic‐Structure Theory by Trygve Helgaker, Poul Jørgensen, Jeppe OlsenModern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory by Attila Szabo and Neil S. Ostlund
Physics:
Additional Resources
Notes and Presentations
Fabian Faulstich: Overview of the Quantum Many-Body Problem
Timothy Lund: Quantum mechanics of the hydrogen atom
Ben Freiman: The hydrogen molecule and the Hartree-Fock method
Michael Papadopoulos: Second quantization I: Fock space, creation and annihiliation operators, Excitation operators
Fabian Faulstich: Recap: the Hartree-Fock method (first quantization)
Edward Lu: Second quantization II: Slater-Condon rules, Wick's theorem, Hartree-Fock revisited additional notes [ pdf ]
Chanaka Mapa Mudiyanselage: The linear combination of atomic orbitals ansatz additional notes [ pdf ]
Talha Aziz Gaussian-type atomic orbitals and high-dimensional integration additional notes [ pdf ]
Ibrahim Abdulazeez Truncating the coupled cluster ansatz and its working equations
Francis Appiah Finding one and all roots to the coupled cluster equations