Prof. Enrico Bertuzzo
Quantum Mechanics II
News/Announcements
- On Monday, April 22nd 2019 there will be no lecture. The lectures will continue regularly on Wednesday, April 24th.
- First oral examination: Tuesday, April 23rd 2019, at 9h30 in "Sala Tiomno", Departamento de Física Matemática. The examination will follow the rules listed below. If you have some superposition with other courses, please let me know ASAP (and in any case, not after Friday, April 12).
- IMPORTANT: The second and final oral examination will take place on Thursday, June 27th, at 09h00 in "Sala Tiomno" (departamento de Física Matemática).
General Infos
Purpose of the course
Quantum Mechanics is one of
the fundamental subjects for any physicist (together with
electromagnetism). In this course we will study more
advanced topics, such as symmetries in QM, identical particles,
scattering, relativistic QM and entangled states.
Lectures
Monday, Wednesday and Thursday
(14h-16h) room 2021
Evaluation
The students will be assigned a subject, and will be given 30 minutes to organize a presentation. After that, the student will present on the blackboard and will answer questions not only about the assigned subject, but also on the other topics seen in the lectures. A good exposition of the assigned subject will roughly count as 70% of the final note.
Equipe
Enrico Bertuzzo, sala 332 ala central
IFUSP
Topics
I will not follow a unique textbook. Some of the topics are however well presented in some textbook, to which we refer the students (see "Recommended textbooks" for the acronyms).
- More on symmetries
- Discrete symmetries: parity, time reversal, discrete translations and Bloch theorem [Sa 4.2, 4.3, 4.4]
- Identical particles
- Quantum indistinguishable particles [Sa 7.1, 7.2]
- Bosons and fermions [WQFT 4.1]
- Examples (diatomic molecules, He atom, construction of the periodic table, color in particle physics) [Sa 7.3, 7.4, 7.5]
- Density matrix and quantum statistical mechanics
- Density operator and entanglement [BS 6.3]
- Reduced density operators and Shannon entropy [BS 6.3]
- Quantum statistical mechanics [BS 6.4]
- Scattering in quantum mechanics
- In and out states [T 2.a, 2.b]
- Cross section [WQFT 3.4]
- Scattering operator and connections to the interaction picture [BS 13.1, 13.2]
- Relativistic quantum mechanics Lecture notes
- Algebra of the Lorentz and Poincarè groups [WQFT 2.3, 2.4]
- Relativistic wave equations (Klein-Gordon and Dirac) and their problems
- Second quantization and the road to quantum field theory Lectures notes
- Fock space [WQFT 4.1, 4.2]
- Momentum and position representations [see for instance M.C. Chang notes]
- Nonrelativistic quantum fields
- Equivalence between second quantization and canonically quantized field theory
- Relativistic quantum fields
Exercises
Exercises for the topics developed during the lectures can be found here.
Recommended textbooks
Here goes a list of book on QM (or quantum field theory, which can be used as reference for relativistic quantum mechanics) that are good for consultation.
- M. Le Bellac, "Quantum Physics" [LB]
- K. Gottfried, T. Yan, "Quantum Mechanics: Fundamentals" [GY]
- J.J. Sakurai, "Modern Quantum Mechanics" [Sa]
- R. Shankar, "Principles of Quantum Mechanics" [Sh]
- S. Weinberg, "Lectures on Quantum Mechanics" [W]
- R. Feynman, A. Hibbs, "Path Integrals and Quantum Mechanics" [FH]
- J. Binney, D. Skinner, "The Physics of Quantum Mechanics" [BS]
- V. P. Nair, "Quantum Field Theory - A Modern Perspective" [N]
- S. Weinberg, "The quantum theory of fields Vol. 1" [WQFT]
- J.R. Taylor, "Scattering theory: the quantum theory of nonrelativistic collisions" [T]
It may also be useful to consult the following online references: