Quantum Mechanics I (2025 Semester 1)
Lectures: Mondays & Thursdays 14:00 - 16:00
Monitoria: Wednesdays 14:00 - 16:00
Room: ???
Monitor: ???
Prof.: Matthew Luzum (Sala 3093)
Exercise lists
Scan/digitize the lists and upload to Moodle by the due date
Homework 1 -- due August 18;
Homework 2 -- due August 25;
Homework 3 -- due September 1;
Homework 4 -- due September 15;
Homework 5 -- due September 22 September 29;
Homework 6 -- due October 6;
Homework 7 -- due October 13;
Homework 8 -- due October 20;
Homework 9 -- due October 27;
Homework 10 -- due November 3;
Homework 11 -- due November 17;
Homework 12 -- due November 24;
Exams
Exam 1 -- October 14???? (Lectures 1-9, Homework 1-5)
Exam 2 -- November 9???? (Lectures 10-18, Homework 6-10)
Final exam -- November 25???? (All lectures and homework lists)
Lectures
August 10-- Structure of Quantum Mechanics: postulates, Hilbert space, operators, commutators, outer product, resolutions of the identity (Shankar ch. 1. Other references: Sakurai ch. 1, Weinberg ch 3, Littlejohn lecture notes, Jaffe lecture notes)
August 13 -- Structure of QM: Operators; Hermitian anti-Hermitian and Unitary operators, spectra, normalizable and non-normalizable states, measurement, uncertainty principle (Shankar Ch. 1, Littlejohn lecture notes, Littlejohn lecture notes)
August 17 -- 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 20 -- Spatial degrees of freedom -- configuration space wavefunctions, spatial translations, momentum space (LIttlejohn notes)
August 24 -- Some topics in 1D wave mechanics; Time evolution (Littlejohn notes)
August 27 -- Harmonic Oscillator (Littlejohn notes)
August 31 -- Path Integrals (Littlejohn notes)
September 3 -- Path Integrals II -- stationary phase approximation, classical limit (Littlejohn notes)
September 7-11 -- No class (Semana da Pátria)
September 14 -- Particle in an electromagnetic field, gauge invariance, Aharonov-Bohm effect (Sakurai Ch 2.7)
September 17 -- Rotations/angular momentum (Sakurai Ch 3, Littlejohn classical rotations, Littlejohn spin-1/2 rotations)
September 21-25 -- No class
September 28 -- Rotations in spin-1/2 systems (Sakurai Ch 3, Littlejohn notes)
October 1 -- Representations, matrix elements, irreducible subspaces (Sakurai Ch 3, LIttlejohn notes)
October 5 -- Orbital angular momentum and spherical harmonics (Sakurai Ch 3, Littlejohn notes)
October 8 -- Monitoria
October 12 -- No class (Nossa Senhora Aparecida)
October 14 -- Exam 1 (Lecture 1-9, Homework 1-5)
October 19 -- Central potentials (Littlejohn notes, Sakurai Ch. 3)
October 22 -- Coulomb potential, Hydrogen atom, (Sakurai Ch. 3.7 and 4.1), addition of angular momentum (Littlejohn notes, Sakurai Ch. 3)
October 26 -- Clebsch-Gordon Coefficients, tensor operators, irreducible tensor operators, spherical tensor operators (Sakurai Ch. 3.11, Littlejohn notes)
October 29 -- tensor operators, products of spherical tensor operators (Sakurai Ch. 3.11, Littlejohn notes)
November 2 -- No class (Finados)
November 4 -- Wigner-Eckart theorem (Sakurai Ch. 3.11, Littlejohn notes)
November 5 -- Monitoria
November 9 -- Exam 2 (Lectures 10-18, Homework 6-10 -- rotations and angular momentum)
November 11 -- time-independent perturbation theory; nondegenerate (Sakurai Ch. 5)
November 12 -- degenerate time-independent perturbation theory, variational method (Sakurai Ch. 5)
November 16 -- time-dependent perturbation theory, Dyson series (Littlejohn notes, Sakurai Ch 5)
November 19 -- fine structure of the hydrogen atom (LIttlejohn notes)
November 23 -- Monitoria
November 25 -- 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