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Black body theory. Aspects of corpuscular radiation. Atomic models. Heisenberg's uncertainty principle. Wave packet and wave-particle duality.

Schroedinger wave mechanics. Eigenvalue equation for Hermitian operators. Pure states. Properties of the discrete spectrum of non-degenerate Hermitian operators. Degenerate discrete spectrum. Continuous spectrum. Mixed spectrum. Unitarity transformations. Stationary states and their properties. One-dimensional problems. Potential well. One-dimensional quantum harmonic oscillator. Landau and E. Lifsits, title: Meccanica quantistica, teoria non relativistica, Vol.

III, editor: Editori Riuniti. There is also the english version. Educational objectives The course is the first module of Quantum Mechanics. The main objective is to provide students with the basic knowledge necessary to address the study of quantum mechanics. The main knowledge gained will be: Basic facts about the crisis of classical physics and the theory of black body radiation. Concept of wave function. Eigenvalue equations. Properties of spectra for Hermitian operators. Unidimensional problems.

Quantum treatment of the one-dimensional harmonic oscillator. The main skills acquired will be: Knowing how to solve the eigenvalue equation for the Hamiltonian. Knowing how to treat one-dimensional problems. Knowing how to solve the eigenvalue equation for the Hamiltonian of the harmonic oscillator. Prerequisites Mathematical methods for physicists Teaching methods face to face lecture and exersises Other information none Learning verification modality Written and oral exam Extended program The crisis of classical physics.

Study of electromagnetic radiation in a isotherm cavity. Kirchhoff theorem. Stefan-Boltzmann's theorem. Rayleigh-Jeans law. Planck's quantization theory. Compton effect. Frank and Hertz experiment. Stern and Gerlach experiment. Wave aspects of particles. Matter waves.

Davisson and Germer experiment. Specific heat at constant volume of crystalline solids and Einstein model. Wilson-Sommerfeld rules for the hydrogen atom. Bohr and Einstein experiments. Superposition principle. Time-dependent Schroedinger equation. Analogy between geometrical optics and classical mechanics.

Solution of the Schroedinger equation for free particles. Interpretation of the Fourier transform of the wave function. Wave function representation in k space. Properties of quantum commutators. Fundamental commutations relations. Simultaneous measurement of two physical observables and common system of eigenfunctions. Time evolution of the wave packet. Time evolution operator and solutions of the Schroedinger equation in the case of time-independent Hamiltonian.

Eigenvalue equation for free particles in space. Hamiltonian with separable variables. Study of one-dimensional problems: the case of the free particle. Scattering of the wave packet for free particle. Scattering of the wave packet of minimum uncertainty. Generic potential. General properties of one-dimensional systems.

Transmission coefficient and reflection coefficient. Step potential of infinite height. Barrier potential. Tunnel effect. Alpha decay of heavy nuclei. Gamow factor. Potential well of infinite depth. Algebraic method for the harmonic oscillator.

Lowering and raising operators. Matrix representation of physical observables on the basis of eigenstates of the harmonic oscillator. Three-dimensionlal problems, central potentials, isotropic harmonic oscillator and hydrogenoid atoms. Time independent and time dependent perturbation theory. Fine structure of hydrogenoid atoms. Zeeman effect Reference texts L. The main aim of this teaching is to provide students with the bases needed to address and solve the most important problems in quantum mechanics.

Main knowledge acquired will be: Knowledge of the solutions of the eigenvalues equations for angular momentum operators. Knowledge of series solutions of second order differential equations.

Perturbative and variational methods. The main competence i. Treatment of the eigenvalue problem with central potentials. Teaching methods Lectures and exercises Other information none Learning verification modality written and oral exam.

Extended program Angular momentum operators Li and their commutators. Three-dimensional problems. Separation of variables in Cartesian and spherical coordiantes. Radial equation and its treatment for a generic potential. Isotropic harmonic oscillator.

Two body problem. Separation of the center of mass motion. Hydrogenoid atoms: energy eigenvalues and eigenfunctions. Intrinsic angular momentum: spin. Pauli's theory of spin. Angular momentum composition. Clebsh-Gordan coefficients. Identical particles and their indistinguibility in a quantum theory.

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