Introductory quantum physics

04 Nov 2025 (2h 00m)

GIUSEPPE La Rocca - Course (teaching activity) - Face to face

Lezione 1-2 : wave-particle duality and uncertainty principle, two-slits interference, photoelectric effect

06 Nov 2025 (2h 00m)

STEFANO Luin - Course (teaching activity) - Both face to face and online

Functions. Cartesian plane, points, lines; line through two points. Derivatives, differentials; chain rule. Potential energy (U) and forces (F) in 1D: from the U to the F graphs. Kinetic and total energies for a mass point. Partial and total derivatives of functions of more than one variable. Dot-notation for total derivatives with respect to times. Complex numbers, conjugation, modulus; imaginary exponentials, trigonometric functions, unit circle, complex plane.

07 Nov 2025 (2h 00m)

GIUSEPPE La Rocca - Course (teaching activity) - Face to face

Lezione 3-4: classical wave equation, diffraction and interference, standing waves

11 Nov 2025 (2h 00m)

GIUSEPPE La Rocca - Course (teaching activity) - Face to face

Lezione 5-6: probabilistic interpretation of the wave function, Schrödinger equation, stationary states

13 Nov 2025 (2h 00m)

STEFANO Luin - Course (teaching activity) - Both face to face and online

Euler identity and identities in trigonometry. Many-valued root functions in the complex field; multiplication as "rotation" in the complex plane. Polynomials. Integral as the "inverse" of derivative; integrals of elementary functions. Linear differential equations: checking their solutions (and determining their parameters); solutions for the classical and damped harmonic oscillator.

14 Nov 2025 (2h 00m)

GIUSEPPE La Rocca - Course (teaching activity) - Face to face

Lezione 7-8: 1D time independent Schroedinger equation: potential step and potential barrier, reflection and transmission amplitudes, tunneling

18 Nov 2025 (2h 00m)

GIUSEPPE La Rocca - Course (teaching activity) - Face to face

Lezione 9-10: 1D quantum well, 2D quantum well, 1D harmonic oscillator

20 Nov 2025 (2h 00m)

STEFANO Luin - Course (teaching activity) - Both face to face and online

Fourier transforms, anti-Fourier transforms, translations in direct space, Dirac Delta for proving antiFourier transform. Approximations in physics and their validity. Quantum wells. Meaning of time and space phase changing in wavefunctions. Origin of boundary conditions in steps-potential 1D problems; validity of infinite well approximation. Dirac delta; boundary conditions with Dirac-delta-like potentials.

21 Nov 2025 (2h 00m)

GIUSEPPE La Rocca - Course (teaching activity) - Face to face

Lezione 11-12: symmetric double well, hermitian operators, eigenvalues and eigenfunctions, expectation values

25 Nov 2025 (2h 00m)

GIUSEPPE La Rocca - Course (teaching activity) - Face to face

Lezione 13-14: measurement process, commutators, uncertainty relations

27 Nov 2025 (2h 00m)

STEFANO Luin - Course (teaching activity) - Both face to face and online

Solutions for 1D Schrödinger equation with steps-potentials; exact solution for the ground state wavefunction of a negative-Dirac-delta potential. Theoretical basis on algebraic groups. Exercise on invertible functions on a domain as a group with the operator of function composition, inverse. Vectorial spaces: formal properties; scalar product (also in complex field); norm. Space spanned by a set of vectors. Vectorial space dimension and independent vectors (exercise). Bra-Ket notation.

02 Dec 2025 (2h 00m)

GIUSEPPE La Rocca - Course (teaching activity) - Face to face

Lezione 15-16: time evolution, conserved quantities and good quantum numbers, transition rate and lifetime

04 Dec 2025 (2h 00m)

STEFANO Luin - Course (teaching activity) - Both face to face and online

Cosine of angle amongst two vectors; equivalence of definitions in R^2. Versors, orthonormal bases and orthonormalization of a basis. Determination of the components of a vector with orthonormal bases. Operators and functionals: fundamentals, nonlinear and linear operators; matrices as linear operators, product of matrices (hints); bra as a functional. Infinite dimensional vectorial spaces.

05 Dec 2025 (2h 00m)

GIUSEPPE La Rocca - Course (teaching activity) - Face to face

Lezione 17-18: classical atomic models and their shortcomings, Rutherford experiment, Franck-Hertz experiment, quantum angular momentum

09 Dec 2025 (2h 00m)

GIUSEPPE La Rocca - Course (teaching activity) - Face to face

Lezione 19-20: hydrogen atom, good quantum numbers, spectrum and electronic orbitals

11 Dec 2025 (2h 00m)

STEFANO Luin - Course (teaching activity) - Both face to face and online

Discussion of exam modalities. Hermitian operators and observables. Recall of measurements in quantum mechanics, expected values. Exercise: sequential measurements of non-commuting observables, probabilities of the results of measurements. Negative-delta potential: estimate of ground state energy and typical wavefunction dimension (exercise); average value of an operator on a wavefunction.

12 Dec 2025 (2h 00m)

GIUSEPPE La Rocca - Course (teaching activity) - Face to face

Lezione 21-22: Zeeman effect, Stern-Gerlach experiment and electron spin, singlet and triplet states

16 Dec 2025 (2h 00m)

GIUSEPPE La Rocca - Course (teaching activity) - Face to face

Lezione 23-24: Helium atom, mean field approximation, polyelectronic atoms, periodic table of the elements

13 Jan 2026 (2h 00m)

GIUSEPPE La Rocca - Course (teaching activity) - Face to face

lezione 25-26: adiabatic approximation for molecules, hydrogen molecule, MO-LCAO

20 Jan 2026 (2h 00m)

GIUSEPPE La Rocca - Course (teaching activity) - Face to face

lezione 27-28: biatomic molecules, hybrid orbitals of carbon, polyatomic molecules

23 Jan 2026 (2h 00m)

GIUSEPPE La Rocca - Course (teaching activity) - Face to face

Lezione 29-30: molecular vibrations and rotations, molecular spectroscopy