STRUCTURE OF MATTER
(Advanced Quantum Physics)

The lecturer can be contacted via e-mail: luca.salasnich@unipd.it The video lectures can be found (free of charges for University students) in the Federica Web Learning platform.

Syllabus The course consists of 48 hours: 36 hours of theory and 12 hours of exercises. The exam will be a colloquium at the blackboard with chalk, where the student will discuss two topics chosen on the spot by the examination board. Please, do the exam ONLY IF you really know ALL THE TOPICS of the course. The student MUST really know the meaning of the symbols she/he wrote at the blackbord: it is not enough to memorize the formulas and the text of book and lecture notes. It is necessary to really know the physical and mathematical meaning of the formulas. The student MUST KNOW VERY WELL differential and integral calculus. Please, do not say that you must pass the exam because otherwhise you will lose your fellowship. Please, do not stress the examiners with protests and complaints. The topics of the course are: Second quantization of the electromagnetic field (6+2 hours) Properties of the classical electromagnetic field in the vacuum. Coulomb Gauge. Expansion in plane waves of the vector potential. Quantum oscillators and quantization of the electromagnetic field. Fock states and coherent states of the electromagnetic field. Electromagnetic field at finite temperature. Casimir effect. Electromagnetic transitions (8+4 hours) An atom in the presence of the electromagnetic field. Fermi golden rule. Dipole approximation. Absorption, stimulated and spontaneus emission of radiation: Einstein coefficients. Selection rules. Lifetime of atomic states and linewidths. Population inversion and laser light. The Spin of the Electron (4+2 hours) Klein-Gordon and Dirac equations. The Pauli equation and the spin. Dirac equation with a central potential. Relativistic hydrogen atom and fine splitting. Atoms with many electrons and quantum many-body theory (8+6 hours) Identical particles. Bosons and Bose-Einstein condensation. Fermions and Pauli exclusion principle. Variational principle. Hartree variational method for bosons and the Gross-Pitaevskii equation. Hartree-Fock variational method for fermions. Density functional theory: theorems of Hoemberg-Kohn, density functional of Thomas-Fermi-Dirac-Von Weizsacker and density functional of Khom-Sham. Quantum Schrodinger field (6+2 hours) Field operators for bosons and fermions. Fock and coherent states of the bosonic field operator. Schrodinger field at finite temperature. Matter field for interacting bosons and fermions. Bosons in a double-well potential and the two-site Bose-Hubbard model.

Main book [T] Luca Salasnich, Quantum Physics of Light and Matter (Springer, 2017). Other books [AT1] F. Mandl and G. Shaw, Quantum Field Theory (Wiley, New York, 1984). [AT2] B.H. Bransden and C.J. Joachain, Physics of Atoms and Molecules, 2nd edition (Prentice Hall, Upper Saddle River, 2003). Books for further reading [A1] M.O. Scully and M.S. Zubairy, Quantum Optics (Cambridge Univ. Press, Cambridge, 1997). [A2] R.W. Robinett, Quantum Mechanics: Classical Results, Modern Systems, and Visualized Examples (Oxford Univ. Press, Oxford, 2006). [A3] K. Huang, Statistical Mechanics (Wiley, New York, 1987). [A4] J.D. Bjorken and S.D. Drell, Relativistic Quantum Mechanics (McGraw-Hill, New York, 1964). [A5] E. Lipparini, Modern Many-Particle Physics: Atomic Gases, Quantum Dots and Quantum Fluids (World Scientific, Singapore, 2003). [A6] A. Altland and B. Simons, Condensed Matter Field Theory (Cambridge Univ. Press, Cambridge, 2006). [A7] M. Le Bellac, A Short Introduction to Quantum Information and Quantum Computation (Cambridge Univ. Press, Cambridge, 2006). [A8] L. Maccone, L. Salasnich, Meccanica Quantistica, Caos e Sistemi Complessi (Carocci, Roma, 2008). Slides Lesson 1 Second Quantization of Light unit 1.1 Electromagnetic waves unit 1.2 Quantization of the electromagnetic field Lesson 2 Quantum Properties of Light unit 2.1 Fock states vs Coherent states unit 2.2 Gas of photons and Planck law unit 2.3 Casimir effect Lesson 3 Matter-Radiation Interaction unit 3.1 Minimal coupling and dipole approximation unit 3.2 Fermi golden rule and spontaneous emission unit 3.3 Absorption and stimulated emission Lesson 4 Electromagnetic Transitions unit 4.1 Selection rules and Einstein equations unit 4.2 Line width of electromagnetic transitions Lesson 5 Relativistic Wave Equations unit 5.1 Klein-Gordon and Dirac equations unit 5.2 Pauli equation and the spin unit 5.3 Energy spectrum of the relativistic hydrogen atom Lesson 6 Quantum Many-Body Systems unit 6.1 Identical particles, bosons and fermions unit 6.2 Uniform Fermi gas of non-interacting electrons unit 6.3 Hartree-Fock method for interacting bosons and fermions Lesson 7 Superfluids unit 7.1 Gross-Pitaevskii equation unit 7.2 Equations of superfluid hydrodynamics Lesson 8 Density Functional Theory unit 8.1 Thomas-Fermi density functional unit 8.2 Hoemberg-Kohn theorem and Kohn-Sham density functional Lesson 9 Second Quantization of Matter unit 9.1 Schrodinger field for bosons and fermions unit 9.2 Statistical physics of non-interacting bosons and fermions unit 9.3 Hamiltonian in second quantization with interaction Lesson 10 Bosons in a Double-Well Potential unit 10.1 Two-site Bose-Hubbard Hamiltonian unit 10.2 Josephson equations