Quantum Mechanics I (2025 Semester 1)
Lectures: Mondays & Thursdays 14:00 - 16:00
Monitoria: Wednesdays 14:00 - 16:00
Room: 2005
Monitor: Gabriel Guimarães (gabriel.alg@usp.br)
Prof.: Matthew Luzum (Sala 3093)
Whatsapp group
Exercise lists
Scan/digitize the lists and upload to Moodle by the due date
Homework 1 (Solutions) -- due August 18;
Homework 2 (Solutions) -- due August 25;
Homework 3 (Solutions) -- due September 1;
Homework 4 (Solutions) -- due September 15;
Homework 5 (Solutions) -- due September 22;
Homework 6 (Solutions) -- due September 29;
Homework 7 (Solutions) -- due October 9;
Homework 8 (Solutions) -- due October 16;
Homework 9 (Solutions) -- due October 23;
Homework 10 (Solutions) -- due October 27;
Homework 11 (Solutions) -- due October 29;
Homework 12 (Solutions) -- due November ;
Exams
Exam 1 -- October 1??? (Lectures 1-10, Homework 1-5)
Prova 2 -- November 6??? (Lectures 11-17, Homework 6-10)
Prova final -- November 26??? (All lectures and homework lists)
Lectures
August 11-- Structure of Quantum Mechanics: postulates, Hilbert space (Shankar ch. 1. Other references: Sakurai ch. 1, Weinberg ch 3, Littlejohn lecture notes, Jaffe lecture notes)
August 14 -- Structure of QM: Operators; commutators, outer product, resolutions of the identity, Hermitian anti-Hermitian and Unitary operators, spectra (Shankar Ch. 1, Littlejohn lecture notes)
August 18 -- Structure of QM: Normalizable and non-normalizable states, measurement, uncertainty principle (Sakurai Ch. 1, Littlejohn lecture notes)
August 21 -- Application of postulates to a physical system -- Stern-Gerlach experiment; Mixed states and the density operator (Littlejohn Stern-Gerlach , Littlejohn density operator, Sakurai Ch. 1); Spatial degrees of freedom -- configuration space wavefunctions (LIttlejohn notes)
August 25 -- Spatial degrees of freedom -- configuration space wavefunctions, spatial translations, momentum space (LIttlejohn notes)
August 27 -- Some topics in 1D wave mechanics; Time evolution (Littlejohn notes)
August 28 -- Harmonic Oscillator (Littlejohn notes)
September 1-5 -- No class (Holy Week)
September 8, 10, 11 -- Monitorias?
September 15, 17, 18 -- Monitorias?
September 22 -- Path Integrals (Littlejohn notes)
September 24 -- Path Integrals II -- stationary phase approximation, classical limit (Littlejohn notes)
September 25 -- Particle in an electromagnetic field, gauge invariance, Aharonov-Bohm effect (Sakurai Ch 2.7)
September 29 -- Monitoria
October 1 -- Exam 1 ?? (Lecture 1-10, Homework 1-5)
October 2 -- Rotations/angular momentum (Sakurai Ch 3, Littlejohn classical rotations, Littlejohn spin-1/2 rotations)
October 6 -- Rotations in spin-1/2 systems (Sakurai Ch 3, Littlejohn notes)
October 9 -- Representations, matrix elements, irreducible subspaces (Sakurai Ch 3, LIttlejohn notes)
October 13 -- Orbital angular momentum and spherical harmonics (Sakurai Ch 3, Littlejohn notes)
October 16 -- Central potentials (Littlejohn notes, Sakurai Ch. 3)
October 20 -- Coulomb potential, Hydrogen atom, (Sakurai Ch. 3.7 and 4.1), addition of angular momentum (Littlejohn notes, Sakurai Ch. 3)
October 23 -- Clebsch-Gordon Coefficients, tensor operators, irreducible tensor operators, spherical tensor operators (Sakurai Ch. 3.11, Littlejohn notes)
October 27 -- No class (Dia do Funcionário Público)
October 29 -- products of spherical tensor operators, Wigner-Eckart theorem (Sakurai Ch. 3.11, Littlejohn notes)
October 30 -- Monitoria
November 3 -- Exam 2 ?? (Lectures 11-17, Homework 6-10 -- rotations and angular momentum)
November 5 -- degenerate time-independent perturbation theory, variational method (Sakurai Ch. 5)
November 6 -- fine structure of the hydrogen atom (LIttlejohn notes)
November 10 -- time-independent perturbation theory; nondegenerate (Sakurai Ch. 5)
November 13 -- time-dependent perturbation theory, Dyson series (Littlejohn notes, Sakurai Ch 5)
November 17 --
November 19 --
November 26 -- Final exam ?? (All lectures and homework lists)
Sugested texts
Sakurai: Modern Quantum Mechanics
Shankar: Principles of Quantum Mechanics
Weinberg: Lectures on Quantum Mechanics
Evaluation
The final grade will be based on homework lists (10%) and the two best scores of the three exams (45% each).
Exams 1 and 2 will each cover ~50% of the material, and the final exam will cover the entire semester. The lowest of the three exam scores will be ignored and the two remaining exams will determine 90% of your final grade.
Program
General structure of quantum mechanics
Examples
Angular momentum / spin
Approximation methods
Lecture notes
.Notes from previous class