Lecture
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09 Nov 2022 (2h 00m)
Stefano Luin - Course (teaching activity) - Face to face
Cartesian plane, points, lines; line passing through two points. Derivatives, differentials, derivatives of elementary functions, of sums and products of functions, 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.
16 Nov 2022 (2h 00m)
Stefano Luin - Course (teaching activity) - Face to face
Theoretical basis on "algebraic" groups and fields. Exercises (made interactively) on: demonstration of unicity; invertible functions on a domain as a group with the operator of function composition, inverse. Complex numbers, exponential of complex numbers, conjugation, modulus, root extraction; exercises on imaginary exponentials, trigonometric functions and identities, unit circle, complex plane.
22 Nov 2022 (2h 00m)
Stefano Luin - Course (teaching activity) - Both face to face and online
Many-valued root functions in complex field; multiplication as "rotation" in the complex plane. 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. Negative-delta potential: estimate of ground state energy and typical wavefunction dimension; boundary conditions with Dirac-delta-like potentials; exact solution for the ground state wavefunction of a negative-Dirac-delta potential.
23 Nov 2022 (2h 00m)
Stefano Luin - Course (teaching activity) - Both face to face and online
Vectorial spaces: formal properties; scalar product (also in complex field); norm. Vectorial space dimension and independent vectors (exercise). Definition of cosine of angle amongst two vectors. Orthonormal bases and orthonormalization of a basis (exercise). Kronecker delta and Dirac delta. Bra-ket notation.
30 Nov 2022 (2h 00m)
Stefano Luin - Course (teaching activity) - Face to face
Determination of the components of a vector with orthonormal bases. Infinite dimensional vectorial spaces, with discrete and continuous bases. Fourier series as a basis for L^2 periodic functions. Operators: fundamentals, nonlinear and linear operators, derivative and integral as operators, composition of operators, operators of symmetrization and antisymmetrization of a function (projection operators); matrices (hints). Sum with Einstein notation.
20 Jan 2023 (2h 00m)
Stefano Luin - Course (teaching activity) - Face to face
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. Vectorial product, Levi-Civita tensor, determinant of a matrix (hints). Scalar and vectorial fields; gradient, divergence, curl, Laplacian. Isovalue surfaces and field lines. Coulomb force and potential. Exercise on antisymmetrization and symmetrization as projection operators.
02 Feb 2023 (2h 00m)
Stefano Luin - Course (teaching activity) - Both face to face and online
Calculating the potential knowing an eigenfunction. Average value and probability distribution of p on the wavefunction theta(x)exp(-kx). Lorentzian distribution, recall on Dirac delta, Heavyside theta, and Fourier transform.
16 Feb 2023 (2h 00m)
Stefano Luin - Course (teaching activity) - Both face to face and online
Operators as matrices; transpose, adjoint, multiplication of matrices, determinant. Kronecker delta and Dirac delta (recall). Sx in Sz eigenvector basis. Double quantum wells (delta-like potential) solved as in perturbative theory.
07 Mar 2023 (2h 00m)
Stefano Luin - Course (teaching activity) - Face to face
Exam "simulation": hydrogen molecule (dynamic variables in Hamiltonian, fermions and bosons, angular momenta composition); expectation value and eigenvalues in measurement process; photoelectric effect. Discussion on Stern-Gerlach experiment.
04 May 2023 (2h 00m)
Stefano Luin - Course (teaching activity) - Face to face
Clarifications to questions, discussions, and exercises on: transmission and reflection from 1D barrier; Millikan experiment on photovoltaic effect; selection rules for vibrational modes and degrees of freedom of a molecule; measurements and expected values; Stern-Gerlach experiment; estimation of energy and length scale for the hydrogen atom; Pauli exclusion principle, electronic configurations in atoms and in the hydrogen molecules (hints).
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