# Quantum Mechanics

## Course information

Code: MAT1723HF/APM421H1F

Instructor: Marco Gualtieri

Class schedule: F2-5 MP137

Evaluation: Evaluation will be through bi-weekly assignments

TA: Nikita Nikolaev

## Assignments

## Resources

### Books

The course will draw from a variety of sources, including the recommended texts listed below.

- Quantum Mechanics for Mathematicians, Takhtajan.
- Quantum Theory, Groups and Representations: An Introduction, Woit.
- Lectures on Quantum Mechanics for Mathematics Students, Faddeev and Yakubovskii.
- Quantum Field Theory: A Tourist Guide for Mathematicians, Folland.
- Mathematical Concepts of Quantum Mechanics, Gustafson and Sigal.
- The Theory of Groups and Quantum Mechanics, Weyl.
- The Principles of Quantum Mechanics, Dirac.
- Quantum Mechanics and Integrals, Feynman & Hibbs.

### Articles

- “Topological quantum field theory”, Atiyah.
- “Supersymmetry and Morse theory”, Witten.
- “Anharmonic Oscillator”, and Part II Bender and Wu.

## Main topics

The purpose of this course is to introduce the main phenomena of Quantum Mechanics and to introduce, in parallel, the mathematical structures and ideas which allow us to model and understand these phenomena.

We hope to cover most of the topics below:

- Quantum states, their measurement and evolution
- Amplitudes and probability
- Hilbert Spaces and Unitary representations
- Observables, operators and the uncertainty principle
- Classical vs Quantum mechanics
- SchrÃ¶dinger equation
- WKB method
- Perturbation Theory and Feynman diagrams
- Multi-particle systems and entanglement
- Spin and Statistics; Fermions
- Quantum information theory
- Supersymmetry
- Passing from QM to QFT