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Presentazione
Insegnamento obbligatorio per la Laurea Magistrale in Physics of Complex Systems, collocato al I pd del I anno. In questo insegnamento vengono introdotti i concetti fondamentali della meccanica quantistica e statistica, con alcuni cenni di teoria dei campi e alcune applicazioni specifiche a sistemi a bassa temperatura.
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Risultati di apprendimento attesi
Lo studente deve acquisire una conoscenza approfondita degli elementi di base della meccanica quantistica (equazione di Schrödinger, osservabili, problemi classici risolubili esattamente).
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Prerequisiti / Conoscenze pregresse
Nessuno.
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Programma
- Classical black body radiation theory, photons and Planck energy distribution;
- Thomson atomic theory, Rutherford experiment, calculation of the classical atom life time, photoelectric and Compton effects;
- Waves and Particles: diffraction and interference of photons and electrons;
- Probability amplitudes and probability, superposition principle, probabilistic interpretation of the measurements, observables;
- Vector spaces of |BRA > and
- Eigenvectors and eigenvalues of operators; physical observables as hermitian operators; discrete and continous representations; the Dirac delta;
- Poisson parentheses and commutators; canonical quantization; space and time translation operators;
- Eigenvectors and eigenvalues of the momentum, indetermination principle;
- Schödinger equation, conserved quantities and stationary states;
- One dimensional problems, tunnel effect, probability current and density, current conservation;
- Harmonic oscillator in the Dirac representation, coherent states;
- Angular momentum as generator of space rotations; eigenvectors and eigenvalues of the angular momentum; commutation relation of scalars and vectors with the angular momentum operator; angular momentum in spherical coordinates;
- Combination of angular momenta in quantum mechanics;
- Schödinger equation in three dimensions; central potentials and the hydrogen atom, 3D harmonic oscillator;
- Spin and Pauli Hamiltonian; magnetic moment of a particle with spin; Zeeman and spin-orbit effect;
- Identical particles in quantum mechanics; fermions and bosons; construction of a wave function for a system of N identical particles; Slater determinant, elements of second quantization;
- Time independent perturbation theory;
- Time dependent perturbation theory, Fermi golden rule.
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Testi richiesti o raccomandati: letture, dispense, altro materiale didattico
- P.A.M. Dirac, The Principles of Quantum Mechanics (Oxford University Press, USA) or Principi della Meccanica Quantistica (Boringhieri);
- J.J. Sakurai, Modern Quantum Mechanics (Addison Wesley) or Meccanica Quantistica Moderna (Zanichelli);
- Landau-Lifshitz, Quantum Mechanics Non-Relativistic Theory, Third Edition: Volume 3 (Butterworth/Heineman) or Meccanica Quantistica Non-relativistica (Editori Riuniti);
- R. Feynmann, et al., Lectures on Physics (Vol. III), Addison-Wesley Pub.;
- A. Messiah, Mecanique Quantique, (Donod, Paris) or Quantum Mechanics, (North Holland, Amsterdam).
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Criteri, regole e procedure per l'esame
L'esame consisterà in una prova orale sul programma del corso, o in alternativa nella discussione di un approfondimento svolto dallo studente su un argomento inerente il programma.
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Statistiche superamento esami
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Programma definitivo per l'A.A.2011/12
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