Modern Physics and Quantum Mechanics (QUANTUM MECHANICS PART)

--Quantum mechanics in more than one dimension
+Direct product spaces
+Separable potentials
+The two-bosy problem and central problems
--Angular momentum
+Rotations and angular momentum
+The angular momentum operator and its spectrum
+Spin
+Addition of anular momenta
--Three-dimensional problems
+The radial Schrödinger equation
+The isotropic harmonic oscillator
+The Coulomb potential and the hydrogen atom
--The classical limit of quantum mechanics
+The action in quantum mechanics
+Lagrangean quantum mechaincs andf the path-integral approach
+The semiclassical (WKB) approximation
--Perturbation theory
+Time-independent perturbation theory
+Time-dependent perturbation theory and the interaction picture
+Introduction to scattering theory
--Identical particles
+Many-particle systems
+Bose and Fermi statistics
+The spin-statistics theorem
--Entanglement
+Quantum statistical mechanics and density matrix
+The Einstein-Podolsky-Rosen paradox and local realism
+Bell inequalities and the measurement problem


Prerequisites and exam

PREREQUISITES: Introductory quantum mechanics in one
dimension. Calculus of several variables and geometry in Cartesian and
sperical coordinates. Introductory Lagragean classical mechanics
EXAM: written. The final grade is obtained combining the outcome of
the two written exams after each of the two semesters of which the
course consists.
Previous written exams (with solutions) can
be found on the courses's web page


REFERENCE MATERIAL

Lecture notes (in Italian):

http://wwwteor.mi.infn.it/~forte/mq/testo/mq.pdf

RECOMMENDED BOOKS:

J.J. Sakurai, Meccanica Quantistica Moderna; Zanichelli (textbook)
F. Schwabl, Quantum Mechanics; Springer (optional reference for computational details)
S. Weinberg, Lectures on Quantum Mechanics; Cambridge U.P. (optional reference for further reading)
K. Gottfried e T.M Yan, Quantum Mechanics: Fundamentals; Springer (optional reference for further reading)
J. Binney e D. Skinner, The Physics of Quantum Mechanics; Oxford U.P. (optional reference for further reading)

Problem and exercise books:
G. Passatore, Problemi di meccanica quantistica elementare; Franco Angeli (elementary)
L. Angelini, Meccanica quantistica: problemi scelti; Springer (elementary)
E. d'Emilio, L. E. Picasso, Problemi di meccanica quantistica; ETS
(elementary and intermediate)
A. Z. Capri, Promlems and Solutions in Nonrelativistic Quantum
Mechanics; World Scientific (elementary, intermediate and avanced)
K. Tamvakis, Problems and Solutions in Quantum Mechanics; Cambridge U.P. (intermediate and avanced)
V. Galitski, B. Karnakov, V. Kogan e V. Galitski, Exploring Quantum
Mechanics; Oxford U.P. (700 problems, mainly intermediate and advanced)

Teachnig methods

Exam: written
Presence in class: required
Teaching form: standard (classroom)

Prerequisites:

Fisica Moderna (Introductory Quantum Mechanics)
Meccanica Analitica (Advanced Classical Mechanics)
Analisi 2 (Calculus of many variables)
Goemetria (Geometry and Linear Algebra)