Ateneo - UPO

Critical Basis of quantum mechanics. Definition of a quantum state, the definition of operators and observables. Formulation of elementary quantum systems. Evolution of quantum systems, perturbative methods. Application to atomic and nuclear systems. Application to quantum computations: both from the hardware point of view and theory point of view.

D. Griffiths - D.F. Schroeter: Introduzione alla meccanica quantistica
Casa 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, physical, and from the point of view of several important applications.

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

Frontal lessons using the blackboard

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 the student will be asked to illustrate two or three themes chosen from the topics covered in class, posing the question from both a physical and mathematical point of view.

- 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.
- The two-body problem.
- Hydrogenoid atoms: eigenvalues and eigenfunctions of the Hamiltonian.
- Dirac formalism. 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.
- Time dependent perturbation theory (basic introduction).
- Systems of identical particles, bosons and fermions, Pauli exclusion principle.
- Density matrix.

- Knowledge and understanding:
acquisition of the theoretical basis of Quantum Mechanics and of its various applications and results.

- Applying knowledge and understanding: Full ability to apply the computation techniques of quantum mechanics where the quantum regime is essential (particle physics, quantum computation, and
radio medical screening NMR, PET, .)

- Communicative Skills: Being able to provide either written or oral details of the computation and of the results for the quantum problems.

- Learning skills: the student will have to acquire a certain mastery in basic quantum mechanics. the use of advanced mathematical tools to expand their knowledge
for advanced courses. Notice that quantum mechanics requires a complete change of thinking paradigm with respect to classical mechanics.