Ateneo - UPO

Crisis of classical physics. Conceptual foundations of quantum mechanics. Definition of quantum states, definition of operators and observables. Formulation of elementary quantum systems, problem solving. Evolution of quantum states, perturbation methods. Applications to atomic and nuclear systems.

D. Griffiths - D.F. Schroeter: Introduzione alla meccanica quantisticaCasa Editrice Ambrosiana- Zanichelli (2023)

Provide the fundamental principles of quantum mechanics, the most relevant results for atomic physics, nuclear and subnuclear physics, from historical, mathematical and physical points of view.

Knowledge of Classical Mechanics, of basic Maths and of Mathematical methods for Physics.

Frontal lessons using the blackboard with the integration of exercises and numerical simulations that require the active participation of the students.

Students with physical disabilities, Learning Disabilities or Special Education Needs can request specific services and tools via the Staff Sviluppo e Coordinamento Carriere e Servizi alle Studentesse e agli Studenti, consulting the University webpage: https://www.uniupo.it/en/services/servicesstudents- physical-or-learning-disabilities Students with disabilities, learning disabilities or special education needs, once they have contacted the University Staff, can refer to the tutor in charge of the course to define the examination modalities, concerning academic aspects.

The exam consists of an oral test, during which students will be typically asked three questions on topics covered in class, requiring them to frame the discussion from both a physical and mathematical perspective. At the end of the oral exam, a final grade (out of 30) is assigned. To pass the test the student must demonstrate that they know and understand the basic concepts and their application to problem solving. A passing grade is achieved if at least two questions are answered satisfactorily. Honors are awarded if the answers to all questions are complete and exhaustive.

The crisis of Classical Physics and the dual 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.Hydrogenoid atoms: eigenvalues and eigenfunctions of the Hamiltonian.Heisenberg states and operators, Heisenberg's equation of motion.Symmetries and conservation laws in Quantum Mechanics.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.

Knowledge and understanding: Study of the theoretical and mathematical bases of quantum mechanics, its applications and results.Ability to apply knowledge and understanding: Full ability to use the calculation techniques of quantum mechanics to formulate physical problems where the quantum regime is essential (e.g. particle physics, quantum computation).Communication skills: Being able to provide both orally and in writing the details of the calculation and the results of the application of quantum methods.Learning skills: Acquisition of a good mastery of the conceptual and formal bases of quantum mechanics, in order to be able to expand one's knowledge in the continuation of studies.