Quantum Mechanics: A graduate course

In summary, these are notes from a graduate quantum mechanics course that cover topics such as fundamentals of quantum mechanics, angular momentum, perturbation theory, and scattering. They also include lectures on quantum field theory and mathematical methods in quantum mechanics. Additional resources on C∗-Algebras, Hilbert C∗-modules, and Poisson deformations are provided, as well as lectures on the mathematical aspects of quantum mechanics.
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A complete set of lecture notes for a graduate quantum mechanics course. Topics covered include fundamentals of quantum mechanics, angular momentum, perturbation theory, and scattering.

by: Richard Fitzpatrick (University of Texas)
 

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David Tong: Lectures on Quantum Field Theory

These notes are based on an introductory course on quantum field theory, given to Part III (i.e. masters level) students in the fall of 2006 and 2007. They were also given at the Perimeter Institure PSI programme in 2009. The full set of lecture notes can be downloaded here. They come in at about 150 pages. Individual sections can be downloaded below. Please email me any typos or comments. Last updated June 2008.

http://www.damtp.cam.ac.uk/user/tong/qft.html

Blechman's notes have moved to http://www.pha.jhu.edu/~blechman/papers/mpri.pdf
 
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Some mathematical QM stuff-

Lecture Notes on C∗-Algebras, Hilbert C∗-modules, and Quantum Mechanics
http://arxiv.org/PS_cache/math-ph/pdf/9807/9807030v1.pdf

Poisson deformations:

http://www.ihes.fr/~maxim/TEXTS/Feynman diagrams and low-dimensional topology.pdf

http://www.ihes.fr/~maxim/TEXTS/Formality conjecture.pdf

Mathematical Methods in QM: With Applications to Shrodinger Operators:
http://www.mat.univie.ac.at/~gerald/ftp/book-schroe/

Lecture Notes on QM-Schulten(elementary)
http://www.ks.uiuc.edu/Services/Class/PHYS481/lecture.html

Advanced QM-Mickelsson, and another one by Teo
http://had.fmf.uni-lj.si/~horvat/physics/index.html

New Insights on Time-Symmetry in QM
http://arxiv.org/abs/0706.1232
 
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1. What is Quantum Mechanics?

Quantum Mechanics is a branch of physics that studies the behavior of matter and energy at a very small scale, such as atoms and subatomic particles. It explains how these particles interact with each other and with electromagnetic radiation.

2. What are the main principles of Quantum Mechanics?

The main principles of Quantum Mechanics include the wave-particle duality, uncertainty principle, superposition, and entanglement. These principles describe the probabilistic nature of quantum systems and how they can exist in multiple states simultaneously.

3. How is Quantum Mechanics different from classical mechanics?

Quantum Mechanics differs from classical mechanics in that it takes into account the wave-like behavior of particles and the probabilistic nature of their interactions. In classical mechanics, objects are described as having definite positions and velocities, while in quantum mechanics, these properties are described by probability distributions.

4. What are some applications of Quantum Mechanics?

Quantum Mechanics has many practical applications, including in the development of new technologies such as computers, lasers, and medical imaging. It is also used in fields such as chemistry, materials science, and cryptography.

5. Is it necessary to have a graduate-level understanding of Quantum Mechanics?

While a basic understanding of Quantum Mechanics is important for anyone studying physics, a graduate-level understanding is necessary for those pursuing a career in the field. It involves advanced mathematical concepts and a deeper understanding of the principles and applications of Quantum Mechanics.

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