Corso di laurea in Fisica

This course aims at giving a complete formulation of the principles of Quantum Mechanics and their applications, at the level of a Bachelor Degree in Physics. The students will achieve a deep knowledge of the basics of Quantum Mechanics, necessary to access the Master Program of studies.

Knowledge and Understanding

At the end of the course, the student will master basic knowledge about the principles of Quantum Mechanics and of its elementary applications, and in particular about:

• Wave Function
• Schrodinger Equation
• Hilbert space
• Angular momentum and spin
• Identical particles
• Perturbation theory

Applying Knowledge and Understanding

At the end of the course, the student will know how to:

• Set up and solve exercises and problems of quantum mechanics
• Employ a proper terminology to describe aforementioned topics.

Making judgements
At the end of the course, the student will be able to formulate a judgement on the application of quantum mechanics to problems of fundamental physics.

Communication skills
At the end of the course, the student will know how to:

• Employ a mathematical formalism to describe a problem concerning quantum physics;
• Present a topic concerning quantum physics, in connection to the aforementioned topics.

Learning skills
At the end of the course, the student will develop the capability of self-study and self-evaluation concerning the principles of quantum mechanics and its applications.

Traditional lectures. About two thirds of the time will be used to introduce the various topics, while the remaining  time will be devoted to solving problems. In 2021 the lectures and the exercise sessions will be in the classroom. It will also be possible to follow the lectures in live streaming at 

https://unito.webex.com/meet/paolo.gambino

The student problem-solving abilities will be tested through a written exam. The test must be carried out without the help of textbooks or notes.

The ability to expose clearly the topics covered during the course is tested through an oral exam. The test consists essentially in the presentation of one or two of the topics taught during the course. It always begins with a discussion on the written test. Then the student will be invited to use the blackboard to expose one of the topics covered during the lectures, in an exhaustive but concise way.

The final assessment will take into account both the written test and the oral exam.

Many exercises will be solved during the classes, in preparation of the written test.

 The crisis of Classical Physics and the wave-particle nature of matter and radiation. The wave function and the Schrödinger equation. Plane waves and wave packets. Coordinate space and momentum space. Physical quantities and quantum operators: commutation rules, eigenvalue equations.  Measurements in QM, simultaneous measurement of several quantities, uncertainty principle. Eigenvalues and eigenfunctions of momentum and orbital angular momentum operators.  States of a quantum system, stationary states and time evolution. One-dimensional problems: step potential, potential barrier, potential well, bound states. Linear harmonic oscillator. Central problems. The two-body problem. Hydrogenoid atoms: eigenvalues and eigenfunctions of the Hamiltonian. Dirac formalism. Heisenberg states and operators, Heisenberg's equation of motion. The spin. Composition rules of angular momenta. Case of two spin 1/2. Time independent perturbation theory: stationary states with non degenerate and degenerate discrete energy spectra. Time dependent perturbation theory. Systems of identical particles, bosons and fermions, Pauli exclusion principle. Entanglement, Bell's theorem, density matrix. See detailed program on Moodle.

Reference text:

David J. Griffiths and Darrel F. Schroeter, "Introduction to Quantum Mechanics" Cambridge University Press, Third Edition

Other texts:

Claude Cohen-Tannoudji, Bernard Diu, Frank Laloe "Quantum Mechanics" Wiley

Stefano Forte, Luca Rottoli, "Fisica Quantistica", first edition, Zanichelli