Mathematical Quantum Mechanics — 1^st Semester — 2026/2027

Lecturer:	José Natário

	Email: jnatar@math.tecnico.ulisboa.pt

	Office: Mathematics Building, 4th floor, room 4.29

Classes:	Tuesdays from 10:00 to 11:30 in room E5, and Thursdays from 10:00 to 11:30 in room E5
Office Hours:	Drop by my office or send me an email

Annoucements

Classes start on September 8.

Basic principles: quantization, wave function, Schroedinger equation; observables, operators, probability; Hilbert space.

Spectral theorem: spectral theorem for bounded self-adjoint operators; spectral theorem for unbounded self-adjoint operators.

Symmetries: Wigner's theorem; representations, angular momentum; addition of angular momenta; quantum statistics.

Coherence and decoherence: EPR, quantum entanglement; coherent states; decoherence; quantum-to-classical transition; quantum information.

Geometric quantization: mechanics on symplectic manifolds; line bundles and connections; prequantization; polarizations; geometric quantization.

Main

Secondary