Introductory Quantum Physics

07 Nov 2023 (2h 00m)

Giuseppe La Rocca - Corso (attività didattica) - In presenza

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

10 Nov 2023 (0h 05m)

Stefano Luin - Corso (attività didattica) - In presenza

Cartesian plane, points, lines; line passing through two points. Derivatives, differentials, derivatives of elementary functions and of composition of functions (chain rule). Integral as the "inverse" of derivative. Potential energy (U) and forces (F) in 1D: from the U to the F graphs. Partial and total derivatives of functions of more than one variable. Dot-notation for total derivatives with respect to times. Exercises. Complex numbers, conjugation, modulus; exercises on imaginary exponentials, trigonometric functions and identities, unit circle, complex plane. (NOTE: 2-hour lesson borrowed from the course [lezione da 2 ore mutuata dal corso] "Physical and mathematical fundamentals for biophysics")

14 Nov 2023 (2h 00m)

Giuseppe La Rocca - Corso (attività didattica) - In presenza

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

17 Nov 2023 (2h 00m)

Giuseppe La Rocca - Corso (attività didattica) - In presenza

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

17 Nov 2023 (2h 00m)

Stefano Luin - Corso (attività didattica) - In presenza

Many-valued root functions in the complex field; multiplication as "rotation" in the complex plane. Solutions for the classical harmonic oscillator; derivatives of sums and products of functions; complex "waves" for representing classical ones; checking the solution (and determining their parameters) of differential equation. Total energy of a mass point. Scalar and vectorial fields; gradient and divergence. Isovalue surfaces and field lines.

21 Nov 2023 (2h 00m)

Giuseppe La Rocca - Corso (attività didattica) - In presenza

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

24 Nov 2023 (2h 00m)

Giuseppe La Rocca - Corso (attività didattica) - In presenza

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

24 Nov 2023 (2h 00m)

Stefano Luin - Corso (attività didattica) - A distanza

Exercises on gradient and divergence, derivative operation on compositions and products of functions. Coulomb force and potential. Meaning of time and space phase changing in wavefunctions. Approximations in physics and their validity; origin of boundary conditions in steps-potential 1D problems; validity of infinite well approximation. Dirac delta and Heaviside theta. Boundary conditions with Dirac-delta-like potentials; exact solution for the ground state wavefunction of a negative-Dirac-delta potential.

28 Nov 2023 (2h 00m)

Giuseppe La Rocca - Corso (attività didattica) - In presenza

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

01 Dic 2023 (2h 00m)

Giuseppe La Rocca - Corso (attività didattica) - In presenza

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

01 Dic 2023 (0h 30m)

Stefano Luin - Corso (attività didattica) - In presenza

Discussione sul contenuto del corso. Lezione ridotta dietro richiesta dell'unico studente presente. La lezione può essere mutuata, per quanto riguarda i contenuti, da quella del corso in "Physical and mathematical fundamentals for biophysics" del 5/12/2023 (registrazione su Teams).

05 Dic 2023 (2h 00m)

Giuseppe La Rocca - Corso (attività didattica) - In presenza

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

12 Dic 2023 (2h 00m)

Giuseppe La Rocca - Corso (attività didattica) - In presenza

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

15 Dic 2023 (2h 00m)

Giuseppe La Rocca - Corso (attività didattica) - In presenza

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

15 Dic 2023 (2h 00m)

Stefano Luin - Corso (attività didattica) - In presenza

Equivalence of scalar product definitions (by components and by cosine between two vectors) in R^2 (exercise). Orthonormal bases and orthonormalization of a basis (exercise). Kronecker delta and Dirac delta. Determination of the components of a vector with orthonormal bases. Infinite dimensional vectorial spaces, with discrete and continuous bases (hints). Fourier series as a basis for L^2 periodic functions. Bra-ket notation; operators and functionals: fundamentals, nonlinear and linear operators; matrices (hints). Sum with Einstein notation.

19 Dic 2023 (2h 00m)

Giuseppe La Rocca - Corso (attività didattica) - In presenza

Lezione 21-22: Stern-Gerlach experiment and electron spin, singlet and triplet states, Helium atom, mean field approximation

09 Gen 2024 (2h 00m)

Giuseppe La Rocca - Corso (attività didattica) - In presenza

Lezione 23-24: polyelectronic atoms, periodic table of the elements

09 Gen 2024 (2h 00m)

Stefano Luin - Corso (attività didattica) - Mista

Hermitian operators and observables: an "historical" point of view. 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 Gen 2024 (2h 00m)

Giuseppe La Rocca - Corso (attività didattica) - In presenza

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

16 Gen 2024 (2h 00m)

Giuseppe La Rocca - Corso (attività didattica) - In presenza

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

19 Gen 2024 (2h 00m)

Giuseppe La Rocca - Corso (attività didattica) - In presenza

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