Degree course: 
Corso di First cycle degree in Physics
Academic year when starting the degree: 
Academic year in which the course will be held: 
Course type: 
Compulsory subjects, characteristic of the class
First Semester
Standard lectures hours: 
Detail of lecture’s hours: 
Lesson (64 hours)

Quantum mechanics I. Principles of analytical mechanics and electromagnetism. We will also use mathematical tools introduced in the course of mathematical methods for physics.

Final Examination: 

The exam is divided into two parts:
-a written test (3 hours) consisting in two to three exercises covering the main topics studied in the course, which will test the ability of students in applying the techniques learned in class to problems of nonrelativistic quantum mechanics;
- an oral part, where the understanding of the quantum mechanics basic tools introduced during the course will be assessed.
Each part will be evaluated with a grade in the range 0 to 30, and the final grade will be the average, if greater than or equal to 18, of the grades of the two parts.

Voto Finale

This course is designed to complement the student's knowledge in the field of non-relativistic quantum mechanics, applied to the case of a single particle in force fields. Both exactly solvable problems and approximate methods will be addressed, in order to complete the technical background for the application of quantum mechanics to the basic problems of modern physics.

General theory of angular momentum;
exactly solvable systems; approximate methods.

General theory of angular momentum: orbital angular momentum in quantum mechanics, spherical harmonics, the relationship between the rotations of a system in three-dimensional space and the rotation operators applied to a state in the Hilbert space of the system, rotations for many-particle systems, spin angular momentum, the Pauli spinors, addition of two angular momenta, Clebsch-Gordan coefficients, Wigner-Eckart theorem.

Exactly solvable systems: rotator, quasi-classical states of a rotator, two-dimensional harmonic oscillator, coherent states of a two-dimensional oscillator, charged particle in a uniform magnetic field and Landau levels, motion in a central potential, free motion in three dimensions, three-dimensional harmonic oscillator, Coulomb potential and hydrogen atom.

Approximate methods: scattering processes (partial waves analysis, phase shifts, the Born approximation), time-independent perturbations (nondegenerate perturbation theory, the Rayleigh-Schrödinger expansion, degenerate perturbation theory, applications: the Stark effect, two-level systems), the WKB method, the adiabatic approximation and Berry’s phase.

- Claude Cohen-Tannoudji, Bernard Diu, Franck Laloë, “Quantum Mechanics”, vol. I-II (Wiley).
- David J. Griffiths, “Quantum Mechanics” (Pearson Education International).
Exercises and syllabus available at the web page http://scienze-como.uninsubria.it/benenti/corsi/qm2.html

Lectures, during which the theoretical concepts of the course will be introduced and exercises solved.

Office hours for students: by appointment (giuliano.benenti@uninsubria.it).