Quantum Mechanics II (2025 Semester 1)
Lectures: Mondays & Thursdays 14:00 - 16:00
Discussion/Monitoria: Wednesdays 14:00 - 16:00
Classroom: 2005
TA ("Monitor"): Carla Ribeiro Rodrigues da Rocha
Prof.: Matthew Luzum (office 3097)
Exams
Midterm exam 1 -- April 24
Midterm exam 2 -- June 4 ???
Final exam -- June 18 ???
Lectures
March 10 -- Identical particles: Multiparticle states, evolution of multiparticle states, permutation symmetry, indistinguishable particles, 2 electron system (Sakurai Ch 6, Shankar Ch 10)
March 13 -- Identical particles: more than 2 particles, anyons, Young tableaux (Sakurai Ch 6, Shankar Ch 10)
March 17 -- Identical particles: Helium atom, periodic table, nuclear shell model, continuous symetries + conservation laws (Sakurai 6.4, Shankar 13.4)
March 20 -- Symmetries: Symmetry groups, parity (Sakurai 4, Shankar 11)
March 24--Symmetries: Parity, lattice translation (Sakurai 4, Shankar 11)
March 27 -- Symmetries: Time reversal (Sakurai 4, Shankar 11)
March 31 -- Density operator, Shannon entropy, Von Neumann entropy (Horodecki)
April 3 -- Quantum entanglement, entanglement entropy, EPR, Bell inequalities (Horodecki)
April 7 - 11 -- No class
April 14-18 -- No class (Holy Week)
April 21 -- No class (Tiradentes)
April 24 -- Exam 1
April 28 -- Scattering: Introduction, cross sections, 2-body kinematics
April 30 -- Scattering: Green's function methods -- Lippmann-Schwinger equation (Sakurai 7.1)
May 5 -- Scattering: Born approximation, Optical Theorem (Sakurai 7.2-7.3)
May 7 -- Scattering: Optical Theorem, Partial waves & phase shifts (Shankar 19.5, Sakurai 7.6)
May 12 -- Scattering: Partial waves -- Hard Sphere (Sakurai 7.6-7.7)
May 14 -- Scattering: Partial waves -- Finite spherical well / barrier, Resonance scattering, scattering of identical particles (Sakurai 7.7-7.9)
May 19-- Scattering: Symmetry considerations (Sakurai 7.10), Coulomb scattering (Weinberg 7.9)
May 21-- Scattering: Eikonal approximation (Shajesh notes), General Scattering Theory - S-matrix and Dyson Formula (Weinberg)
May 26 -- Scattering: General Scattering -- S-matrix, Born, Fermi's golden rule, optical theorem (Weinberg)
May 28 -- Monitoria
June 2 -- Não haverá aula (Dia do Funcionário Público)
June 4-- Prova 2
June 9-- Second quantization: Fock space, creation and annihilation operators, number operator, non-relativistic Hamiltonian (Brown: Quantum Field Theory)
June 11 -- Second quantization: momentum space, ground state, equations of motion, relativistic theory, Klein-Gordon equation (Brown)
June 16-- Monitoria
June 18 -- Final exam
June 23 --??
June 25 -- ??
Sugested texts
J.J. Sakurai, "Modern Quantum Mechanics", (chapter numbers refer to Revised edition, not second edition)
A.F.R de Toledo Piza: Mecânica Quântica
Shankar: Principles of Quantum Mechanics
Weinberg: Lectures on Quantum Mechanics
Brown: Quantum Field Theory
Any preferred reference that treats a given topic
Grading
The final grade will be based on the homework lists (10%) and the best 2 scores out of the 3 exams (45% each).
Exams 1 e 2 will each cover ~50% of the material, and the final exam will cover the entire semester. The lowest grade of the three exams will be thrown out and the remaining two exam scores will determine 90% of the final grade.
Program
Identical particles
Symmetries and conservation laws
Scattering Theory
Second quantization
Lecture notes