The need to abandon classical physics. The first five postulates of quantum mechanics. Observables with discrete and continuum spectra. Fundamentals of analytical mechanics: Lagrangian and Hamiltonian. The Dirac postulate. Schroedinger equation. Ehrenfest theorem. Heisenberg principle. Quantum systems in finite dimensional Hilbert spaces. Particle in one dimension: piecewise constant potential, Dirac delta potential, reflection and transmission coefficients, harmonic oscillator and coherent states. Particle in three dimensions: Minimal coupling, continuity equation, angular momentum, spherical harmonics, hydrogen atom. Spin and composition of angular momenta. Perturbation theory for the correction of energy levels. Perturbation theory by temporal evolution.
Co-teaching: Dott. Perfetto Enrico
LEARNING OUTCOMES: The aim of the course is to introduce the student, by means of a theoretical description, to the experiments that have marked the crisis of classical physics and the physical intuitions that led to laying the foundations and developing Quantum Mechanics. It is in this context that we can understand the dynamical, electronic, optical or transport properties of materials. The main educational objectives are the search for eigenvalues and eigenvectors of simple Hamiltonians, such as two-level systems, the quantum harmonic oscillator in one and two dimensions, hydrogen atom, one-dimensional systems such as quantum wells and potential barriers, and finally systems with spin composition. Students will also be able to evolve the wave function over time. In addition, the time-independent perturbation theory, degenerate and non-degenerate cases, and time-dependent, up to the derivation of the Fermi golden rule will also be treated. Short hints are also needed on Analytical Mechanics and Statistical Mechanics, respectively in the opening and closing of the course.
KNOWLEDGE AND UNDERSTANDING:
The theoretical and practical lessons focus on the mathematical derivation and physical interpretation of the postulates of Quantum Mechanics and the resolution of simple models, in order to be able to work on systems with more elaborate Hamiltonians. The course aims to provide the student with the basic tools necessary to solve the Hamiltonian of one of the problems mentioned in the training objectives, knowing how to evolve the wave functions.