Mathematical Foundations of Modern Quantum Many-Body Theory

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Rensselaer Polytechnic Institute MATH 6890, Fall 2024

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This is the official website for course MATH 6890: Mathematical Foundations of Modern Quantum Many-Body Theory in Spring 2025.

This website contains most of the information you need for this course (lecture notes, assignments). Course sensitive information (announcements, exam, grade distribution etc.) will be posted on LMS (Rensselaer credentials required).

General information

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Please read the course syllabus VERY CAREFULLY

Instructor: Fabian M. Faulstich

Lecture: TueFri 10:00AM - 12:00AM Carnegie 101

Office hours: Wed 9 am and Thu 2 pm in 406 Amos Eaton Hall

Piazza page: General questions about the course and its content, which might be of interest to other students, can be asked on the piazza page.

Gradescope page: Homework assignments are to be submitted through Gradescope.

Textbooks

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Mathematics:

A Mathematical Introduction To Electronic Structure Theory by Lin Lin and Jianfeng Lu

Chemistry:

Molecular Electronic‐Structure Theory by Trygve Helgaker, Poul Jørgensen, Jeppe Olsen
Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory by Attila Szabo and Neil S. Ostlund

Physics:

Class materials:

Enter password here to access the class' materials

Lecture notes [pdf] Updated 09/04

Student Presentations

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Presenting 02/25

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Corey Curran - Functional derivative in Hartree-Fock theory to derive the Roothan Haal equations [slides] and [notes]

Jack H. Mandell - Refreaction on single slit [slides] and [notes]

Fansu Meng - Bessel differential equations and their connection to the radial equation for hydrogen

Qingzhou Yu - The H2 molecule bonding v.s. anti-bonding solutions

Chanaka D. Mapa Mudiyanselage - The Clebsch-Gordan coefficients and their connection to spin states [slides] and [notes]

Presenting 02/28

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Muhammad Talha Aziz - General Legendre equations and associated Legendre polynomials [slides] and [notes]

Andrew J. Kraus - Hermite polynomilas [notes]

Ibrahim Abdulazeez - Distribution theory [slides] and [notes]

Felipe M. Cerioni - Direct sums of Hilbert spaces

Alex Moore - Proof of Wick's theorem

Homework Assignments

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Homework assignment 1 [pdf] and [pluto]

Homework assignment 2 [pdf] and [pluto] and [files]

Homework assignment 3 [pdf] and [pluto]

Homework assignment 4 [pdf] and [pluto] and [files]

Homework assignment 5 [pdf] and [pluto]