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Crystal structures and Bravais lattice. Reciprocal lattice. Diffraction and solid crystals, structure factor. Electrons in solids, Bloch's theorem,. Band structure. Tightly and weakly bound electrons. Holes and effective mass. Born-Oppheneimer approximation. Lattice vibrations, phonons, specific heat (Einstein's and Debye's model, density of states). Electrons in metals and interaction with an electromagnetic field (metal transport properties): Drude's and Sommerfeld's models. The semiclassical model Intrinsic and extrinsic semiconductors. Temperature dependence of charge carrier density. Adopted texts N.W. Ashcroft, N.D, Mermin, `Solid State Physics', Holt-Saunders Int. Ed. 1981 C. Kittel, `Introduction to Solid Sate Physics', Wiley, 2004 J. M. Ziman, `Principles of the Theory of Solids', Cambridge University Press, 1979

The course relies on the following prerequisites: 1. CLASSICAL MECHANICS reference text: H. Goldstein, C. P. Poole, and J. L. Safko Classical Mechanics, Addison-Wesley chapter 1 Survey of elementary principles - mechanics of a particle - mechanics of a system of particles - contraints - D’Alambert’s principle and Lagrange’s equations chapter 6 Oscillations - formulation of the problem - the eigenvalue equation and the principal axis transformation - frequencies of free vibration and normal coordinates chapter 8 The Hamilton equations of motion - Legendre transformations and the Hamilton equations of motion chapter 9 Canonical transformations - the equations of canonical transformations - Poisson brackets - Liouville’s theorem 2. CLASSICAL ELECTROMAGNETISM reference text: D. Halliday, R. Resnick, and K. S. Crane Physics - part II, John Wiley & sons chapter 25 Electric charge and Coulomb’s law - electric charge - conductors and insulators - Coulomb’s law - continuous charge distributions - conservation of charge chapter 26 The electric field - the electric field - the electric field of point charges - the electric field of continuous charge distributions chapter 27 Gauss’ law - the flux of the electric field - Gauss’ law chapter 28 Electric potential energy and potential - electric potential energy - electric potential - calculating the potential from the field - potential due to point charges - potential due to continuous charge distributions - calculating the field from the potential - equipotential surfaces - the potential of a charged conductor chapter 29 The electric properties of materials - types of materials - a conductor in an alectric field - ohmic materials - Ohm’s law - an insultatori in an electric field chapter 30 Capacitance - capacitors - capacitance chapter 31 DC circuits - electric current - electromotive force chapter 32 The magnetic field - the magnetic force on a moving charge - circulating charges - the Hall effect 3. QUANTUM MECHANICS reference text: J. J. Sakurai Modern Quantum Mechanics, Addison-Wesley chapter 1 Fundamental concepts - kets, bras, operators - base kets and matrix representation - measurements, observables, and uncertainty relations - position, momentum, and translation - wave functions in position and momentum space chapter 2 Quantum dynamics - time evolution and the Shroedinger equation - the Shroedinger versus the Heisenberg picture - simple harmonic oscillator - Schroedinger’s wave equation chapter 3 Theory of angular momentum - rotations and angular momentum commutation relations - spin 1/2 systems and finite rotations - eigenvalues and eigenstates of angular momentum - orbital angular momentum - addition of angular momenta chapter 4 Symmetry in quantum mechanics - symmetries, conservation laws, and degeneracies - discrete symmetries, parity, or space inversion - lattice translation as a discrete symmetry - the time-reversal discrete symmetry chapter 5 Approximation methods - time independent perturbation theory: non degenerate case - time independent perturbation theory: the degenerate case 4. STATISTICAL MECHANICS reference text: K. Huang Statistical Mechanics, John Wiley & sons chapter 6 Classical statistical mechanics - the postulate of classical statistical mechanics - microcanonical ensemble - derivation of thermodynamics - equipartition theorem - classical ideal gas chapter 7 Canonical ensemble and grand canonical ensemble - canonical ensemble - energy fluctuations in the canonical ensemble - grand canonical ensemble - density fluctuations in the grand canonical ensemble - the chemical potential - equivalence of the canonical ensemble and grand canonical ensemble chapter 8 Quantum statistical mechanics - the postulate of quantum statistical mechanics - ensembles in quantum statistical mechanics - the ideal gases: micro canonical ensemble - the ideal gases: grand canonical ensemble chapter 11 Fermi systems - the equation of state of an ideal Fermi gas chapter 12 Bose systems - photons - Bose-Einstein condensation 5. ATOMIC AND MOLECULAR PHYSICS reference text: B. H Bransden & C. J. Joachain Physics of atoms and molecules, Longman Scientific & Technical chapter 3 One-electron atoms - the Scheoedinger equation for one-electron atoms - energy levels - the eigenfunctions of the bound states chapter 6 Two-electron atoms - the Scheoedinger equation for two-electron atoms - spin wave functions and the role of the Pauli exclusion principle - level scheme of two-electron atoms chapter 7 Many-electron atoms - the central field approximation - the periodic system of the elements chapter 9 Molecular structure - general nature of molecular structure - the Born-Oppenheimer separation for diatomic molecules - electronic structure of diatomic molecules - the structure of polyatomic molecules

N.W. Ashcroft, N.D, Mermin, “Solid State Physics”, Holt-Saunders Int. Ed. 1981
C. Kittel, “Introduction to Solid Sate Physics”, Wiley, 2004
 J. M. Ziman-Principles of the Theory of Solids - Cambridge University Press, 1979


Attendance to the lectures is not mandatory but strongly recommended.

There are two mid-term assessment tests during the course (lasting two hours each). If both tests are passed with a score of at least 15/30 and an average of not less than 18/30, the student is exempted from the written test for the entire academic year.
There are 5 complete calls (written and oral): two in the January/February session, two in the June/July session and one in the September session.
The written test (lasting three hours) includes two problems, each one divided into several questions. The written test is passed with a score of no less than 18/30 and is valid for the session in which it was taken.
The oral exam consists of an interview on the most relevant topics presented in the course. To pass the exam, the student must be able to present arguments and repeat calculations discussed and explained during the course. The student will be asked to apply the methods learned during the course to exercises or to examples and situations similar to those that were discussed in the course.
The evaluation takes into account:
- Correctness and completeness of the concepts discussed by the student;
- clarity and rigor of presentation;
- analytical development of the theory;
- problem-solving skills (method and results).

The final exam grade is determined by the average between the written score (or the average of the mid-term assessment tests) and the oral test score.

Crystal structures and Bravais lattice. Reciprocal lattice. Diffraction and solid crystals, structure factor. Born-Oppheneimer approximation. Lattice vibrations, phonons, specific heat (Einstein’s and Debye’s model, density of states). Electrons in solids, Bloch’s theorem,. Band structure. Tightly and weakly bound electrons. Holes and effective mass. Electrons in metals and interaction with an electromagnetic field (dielectric response, metal transport properties): Drude’s and Sommerfeld’s models. Intrinsic and extrinsic semiconductors. Temperature dependence of charge carrier density. p-n junction. Bravais lattice in 2D and 3D. Primitive vectors and primitive unit cell. Wigner-Seitz unit cell. Conventional unit cell. Basis. Examples: graphene, graphite, cubic lattices (face-centered and body-centered cubic cell). AM: Ch. 4, GPP: Ch. 2.1-2.3, K: Ch. 1 Examples: simple hexagonal and hexagonal close-packed structure. Lattice planes and Miller indexes. Reciprocal lattice as Fourier transform of direct lattice. Examples and Brillouin zone. Family of lattice planes and reciprocal lattice vectors. AM Ch. 4 and 5, K Ch. 1 and 2, GPP Ch. 2.4 and 2.5 Diffraction: x-ray, neutrons and electrons. Laue diffraction and reciprocal lattice. AM: Ch. 6, BG: Ch. 2.1-2.2 K: Ch. 2. Laue and Bragg diffraction. AM: Ch. 6, BG: Ch. 2.1-2.3, K: Ch. 2 Structure factor: geometrical structure factor + atomic form factor (examples). AM: Ch. 6, BG: Ch. 2.4-2.5, K: Ch. 2. Ewald sphere and different experimental configurations. AM: Ch. 6, BG: Ch. 2.7, K: Ch. 2 Structure factor: examples. AM: Ch. 6, BG: Ch. 2.7, K: Ch. 2 Structure factor: examples. AM: Ch. 6, BG: Ch. 2.7, K: Ch. 2 Exercises. AM: Ch. 6, K: Ch. 2. Born-Oppenheimer approximation. GPP: Ch. 8.1 and 8.2, BG: Ch. 3.1, 3.2, 3.3 Motion equations of a linear chain and dynamical matrix. GPP: Ch. 9.1, AM: Ch. 22 Oscillation normal modes: elemental unidimensional lattice. Dispersion relation and density of states. GPP: Ch. 9.1, 9.2, AM: Ch. 22 Oscillation normal modes: unidimensional lattice with basis. Dispersion relation. Acoustic and optical modes. GPP: Ch. 9.1, 9.2, AM: Ch. 22 Summary of acoustic and optical modes in a linear chain with basis. GPP: Ch. 9.1, 9.2, AM: Ch. 22 Exercise on linear chain featuring nth-nearest neighbor interaction. Quantization of the elastic field and phonons (GPP: Ch. 9.4, AM: Ch. 23) Dynamical matrix in three-dimensions (GPP9.3, AM Ch. 22) Dynamical matrix in three-dimensions (GPP9.3, AM Ch. 22). Dynamical matrix in three-dimensions and its Hermitian character (GPP9.3, AM Ch. 22) Specific heat: classical and quantum-mechanical treatment. Debye and Einstein models. AM: Ch. 23, K: Ch. 5, GPP: Ch. 9.5, BG: Ch. 8.1 Debye temperature and chemical trends (examples: diamond, germanium, silicon, graphene). Phonon modes in bidimensional CuO2 Phonon modes in bidimensional square lattice with 1st and 2nd nn interaction. Lecture notes and O. Madelung, Introduction to Solid-State Theory (Ch. 3.3.5). Phonon modes in bidimensional square lattice with 1st and 2nd nn interaction. Lecture notes and O. Madelung, Introduction to Solid-State Theory (Ch. 3.3.5). Specific heat of a two-dimensional square lattice (lecture notes). Bloch’s theorem: I proof (AM Ch 8) Bloch’s theorem: II proof (K Ch. 7) Kronig-Penney model (K Ch. 7) Energy banfìds (K Ch. 7) Central equation (K Ch 7) Central equation and empty lattice approximation(K Ch 7) Weak potential approximation: perturbative approach (AM Ch. 9, K Ch. 7). Weak potential approximation and band gap opening (AM Ch. 9, K Ch. 7) Electron Bragg reflection (AM Ch. 9, K Ch. 7). Metals and insulators (K Ch. 7) Electronic specific heat (AM Ch. 2, K Ch. 6) Sommerfeld integral (AM Ch. 2) Electronic specific heat (AM Ch. 2, K Ch. 6) Tight binding (AM Ch 10) Exercise: weak-electron method in an FCC crystal (AM Ch. 9 ex. 3) Tight binding (AM Ch 10). Exercise: tight binding method applied to a SC crystal Tight binding: polyacetylene bands (lecture notes) Tight binding: graphene bands (lecture notes) Tight binding: graphene bands, Dirac cone, massless relativistic fermions, hexagonal boron nitride (lecture notes) Semiclassical model: motion equations (AM Ch. 12) Semiclassical model: motion equations (AM Ch. 12): filled bands, holes, effective mass Boltzmann equation part I (GPP 11.3) Boltzmann equation part II (GPP 11.3) Static conductivity in metals (GPP 11.4) Semiconductors: main properties (GPP 13.1, AM Ch. 28) Number of carriers in thermal equilibrium: the intrinsic case (AM Ch. 28; GPP 13.1) Effective mass theorem and envelope wavefunction (GPP 13.2) Effective mass theorem and envelope wavefunction (GPP 13.2, BG 11.3.1) and impurities (BG 11.3.1) Conduction band electrons and Landau levels in three dimensions (BG 9.6, GPP 15.2) Doping: donors and acceptors. Level statistics (AM 28, GPP 13.2) Chemical potential and number of carriers vs temperature (AM 28,GPP 13.3) Chemical potential and number of carriers vs temperature (AM 28,GPP 13.3)

Electromagnetism, statistical and quantum mechanics, optics and structure of matter. The course relies on the following prerequisites: 1. CLASSICAL MECHANICS reference text: H. Goldstein, C. P. Poole, and J. L. Safko Classical Mechanics, Addison-Wesley chapter 1 Survey of elementary principles - mechanics of a particle - mechanics of a system of particles - contraints - D’Alambert’s principle and Lagrange’s equations chapter 6 Oscillations - formulation of the problem - the eigenvalue equation and the principal axis transformation - frequencies of free vibration and normal coordinates chapter 8 The Hamilton equations of motion - Legendre transformations and the Hamilton equations of motion chapter 9 Canonical transformations - the equations of canonical transformations - Poisson brackets - Liouville’s theorem 2. CLASSICAL ELECTROMAGNETISM reference text: D. Halliday, R. Resnick, and K. S. Crane Physics - part II, John Wiley & sons chapter 25 Electric charge and Coulomb’s law - electric charge - conductors and insulators - Coulomb’s law - continuous charge distributions - conservation of charge chapter 26 The electric field - the electric field - the electric field of point charges - the electric field of continuous charge distributions chapter 27 Gauss’ law - the flux of the electric field - Gauss’ law chapter 28 Electric potential energy and potential - electric potential energy - electric potential - calculating the potential from the field - potential due to point charges - potential due to continuous charge distributions - calculating the field from the potential - equipotential surfaces - the potential of a charged conductor chapter 29 The electric properties of materials - types of materials - a conductor in an alectric field - ohmic materials - Ohm’s law - an insultatori in an electric field chapter 30 Capacitance - capacitors - capacitance chapter 31 DC circuits - electric current - electromotive force chapter 32 The magnetic field - the magnetic force on a moving charge - circulating charges - the Hall effect 3. QUANTUM MECHANICS reference text: J. J. Sakurai Modern Quantum Mechanics, Addison-Wesley chapter 1 Fundamental concepts - kets, bras, operators - base kets and matrix representation - measurements, observables, and uncertainty relations - position, momentum, and translation - wave functions in position and momentum space chapter 2 Quantum dynamics - time evolution and the Shroedinger equation - the Shroedinger versus the Heisenberg picture - simple harmonic oscillator - Schroedinger’s wave equation chapter 3 Theory of angular momentum - rotations and angular momentum commutation relations - spin 1/2 systems and finite rotations - eigenvalues and eigenstates of angular momentum - orbital angular momentum - addition of angular momenta chapter 4 Symmetry in quantum mechanics - symmetries, conservation laws, and degeneracies - discrete symmetries, parity, or space inversion - lattice translation as a discrete symmetry - the time-reversal discrete symmetry chapter 5 Approximation methods - time independent perturbation theory: non degenerate case - time independent perturbation theory: the degenerate case 4. STATISTICAL MECHANICS reference text: K. Huang Statistical Mechanics, John Wiley & sons chapter 6 Classical statistical mechanics - the postulate of classical statistical mechanics - microcanonical ensemble - derivation of thermodynamics - equipartition theorem - classical ideal gas chapter 7 Canonical ensemble and grand canonical ensemble - canonical ensemble - energy fluctuations in the canonical ensemble - grand canonical ensemble - density fluctuations in the grand canonical ensemble - the chemical potential - equivalence of the canonical ensemble and grand canonical ensemble chapter 8 Quantum statistical mechanics - the postulate of quantum statistical mechanics - ensembles in quantum statistical mechanics - the ideal gases: micro canonical ensemble - the ideal gases: grand canonical ensemble chapter 11 Fermi systems - the equation of state of an ideal Fermi gas chapter 12 Bose systems - photons - Bose-Einstein condensation 5. ATOMIC AND MOLECULAR PHYSICS reference text: B. H Bransden & C. J. Joachain Physics of atoms and molecules, Longman Scientific & Technical chapter 3 One-electron atoms - the Scheoedinger equation for one-electron atoms - energy levels - the eigenfunctions of the bound states chapter 6 Two-electron atoms - the Scheoedinger equation for two-electron atoms - spin wave functions and the role of the Pauli exclusion principle - level scheme of two-electron atoms chapter 7 Many-electron atoms - the central field approximation - the periodic system of the elements chapter 9 Molecular structure - general nature of molecular structure - the Born-Oppenheimer separation for diatomic molecules - electronic structure of diatomic molecules - the structure of polyatomic molecules

AM: N. W. Ashcroft, N. D. Mermin, Solid State Physics, Saunders College Publishing international series. K: C. Kittel, Introduction to Solid State Physics, J. Wiley & Sons, New York GPP: G. Grosso, G. Pastori Parravicini, Solid state physics, Giuseppe Grosso, Giuseppe Pastori Parravicini. - 2. ed. - Oxford : Academic Press, 2014 BG: F. Bassani, U. M. Grassano, Fisica dello Stato Solido, Bollati Boringhieri, Torino

Lectures on theory and exercises in the classroom for the preparation of in itinere tests and written tests. Attendance is optional, but strongly recommended. The course includes lectures on the theory (amounting to approximately 2/3 of the total number of hours dedicated to lecturing), alternated with tutoring sessions (amounting to approximately 1/3 of the total number of hours dedicated to lecturing), during which the methods to solve problems and exercises of the kinds that can be assigned in a written exam are treated.

Attendance to the lectures is not mandatory but strongly recommended.

There are two in itinere tests during the course (lasting two hours each). If both tests are passed with a score of at least 15/30 and an average of not less than 18/30, the student is exempted from the written test for the entire academic year. There are 5 complete calls (written and oral): two in the January/February session, two in the June/July session and one in the September session. The written test (lasting three hours) includes two problems, each one divided into several questions. The written test is passed with a score of no less than 18/30 and is valid for the session in which it was taken. The oral exam consists of an interview on the most relevant topics presented in the course. To pass the exam, the student must be able to present arguments and repeat calculations discussed and explained during the course. The student will be asked to apply the methods learned during the course to exercises or to examples and situations similar to those that were discussed in the course. The evaluation takes into account: - Correctness and completeness of the concepts discussed by the student; - clarity and rigor of presentation; - analytical development of the theory; - problem-solving skills (method and results). The final exam grade is determined by the avergage between the written score (or the average of the in itinere test) and the oral test score.

AM: N. W. Ashcroft, N. D. Mermin, Solid State Physics, Saunders College Publishing international series. K: C. Kittel, Introduction to Solid State Physics, J. Wiley & Sons, New York GPP: G. Grosso, G. Pastori Parravicini, Solid state physics, Giuseppe Grosso, Giuseppe Pastori Parravicini. - 2. ed. - Oxford : Academic Press, 2014 BG: F. Bassani, U. M. Grassano, Fisica dello Stato Solido, Bollati Boringhieri, Torino

Lectures on theory and exercises in the classroom for the preparation of in itinere tests and written tests. Attendance is optional, but strongly recommended. The course includes lectures on the theory (amounting to approximately 2/3 of the total number of hours dedicated to lecturing), alternated with tutoring sessions (amounting to approximately 1/3 of the total number of hours dedicated to lecturing), during which the methods to solve problems and exercises of the kinds that can be assigned in a written exam are treated.

Crystal structures and Bravais lattice. Reciprocal lattice. Diffraction and solid crystals, structure factor. Electrons in solids, Bloch's theorem,. Band structure. Tightly and weakly bound electrons. Holes and effective mass. Born-Oppheneimer approximation. Lattice vibrations, phonons, specific heat (Einstein's and Debye's model, density of states). Electrons in metals and interaction with an electromagnetic field (metal transport properties): Drude's and Sommerfeld's models. The semiclassical model Intrinsic and extrinsic semiconductors. Temperature dependence of charge carrier density. Adopted texts N.W. Ashcroft, N.D, Mermin, `Solid State Physics', Holt-Saunders Int. Ed. 1981 C. Kittel, `Introduction to Solid Sate Physics', Wiley, 2004 J. M. Ziman, `Principles of the Theory of Solids', Cambridge University Press, 1979

The course relies on the following prerequisites: 1. CLASSICAL MECHANICS reference text: H. Goldstein, C. P. Poole, and J. L. Safko Classical Mechanics, Addison-Wesley chapter 1 Survey of elementary principles - mechanics of a particle - mechanics of a system of particles - contraints - D’Alambert’s principle and Lagrange’s equations chapter 6 Oscillations - formulation of the problem - the eigenvalue equation and the principal axis transformation - frequencies of free vibration and normal coordinates chapter 8 The Hamilton equations of motion - Legendre transformations and the Hamilton equations of motion chapter 9 Canonical transformations - the equations of canonical transformations - Poisson brackets - Liouville’s theorem 2. CLASSICAL ELECTROMAGNETISM reference text: D. Halliday, R. Resnick, and K. S. Crane Physics - part II, John Wiley & sons chapter 25 Electric charge and Coulomb’s law - electric charge - conductors and insulators - Coulomb’s law - continuous charge distributions - conservation of charge chapter 26 The electric field - the electric field - the electric field of point charges - the electric field of continuous charge distributions chapter 27 Gauss’ law - the flux of the electric field - Gauss’ law chapter 28 Electric potential energy and potential - electric potential energy - electric potential - calculating the potential from the field - potential due to point charges - potential due to continuous charge distributions - calculating the field from the potential - equipotential surfaces - the potential of a charged conductor chapter 29 The electric properties of materials - types of materials - a conductor in an alectric field - ohmic materials - Ohm’s law - an insultatori in an electric field chapter 30 Capacitance - capacitors - capacitance chapter 31 DC circuits - electric current - electromotive force chapter 32 The magnetic field - the magnetic force on a moving charge - circulating charges - the Hall effect 3. QUANTUM MECHANICS reference text: J. J. Sakurai Modern Quantum Mechanics, Addison-Wesley chapter 1 Fundamental concepts - kets, bras, operators - base kets and matrix representation - measurements, observables, and uncertainty relations - position, momentum, and translation - wave functions in position and momentum space chapter 2 Quantum dynamics - time evolution and the Shroedinger equation - the Shroedinger versus the Heisenberg picture - simple harmonic oscillator - Schroedinger’s wave equation chapter 3 Theory of angular momentum - rotations and angular momentum commutation relations - spin 1/2 systems and finite rotations - eigenvalues and eigenstates of angular momentum - orbital angular momentum - addition of angular momenta chapter 4 Symmetry in quantum mechanics - symmetries, conservation laws, and degeneracies - discrete symmetries, parity, or space inversion - lattice translation as a discrete symmetry - the time-reversal discrete symmetry chapter 5 Approximation methods - time independent perturbation theory: non degenerate case - time independent perturbation theory: the degenerate case 4. STATISTICAL MECHANICS reference text: K. Huang Statistical Mechanics, John Wiley & sons chapter 6 Classical statistical mechanics - the postulate of classical statistical mechanics - microcanonical ensemble - derivation of thermodynamics - equipartition theorem - classical ideal gas chapter 7 Canonical ensemble and grand canonical ensemble - canonical ensemble - energy fluctuations in the canonical ensemble - grand canonical ensemble - density fluctuations in the grand canonical ensemble - the chemical potential - equivalence of the canonical ensemble and grand canonical ensemble chapter 8 Quantum statistical mechanics - the postulate of quantum statistical mechanics - ensembles in quantum statistical mechanics - the ideal gases: micro canonical ensemble - the ideal gases: grand canonical ensemble chapter 11 Fermi systems - the equation of state of an ideal Fermi gas chapter 12 Bose systems - photons - Bose-Einstein condensation 5. ATOMIC AND MOLECULAR PHYSICS reference text: B. H Bransden & C. J. Joachain Physics of atoms and molecules, Longman Scientific & Technical chapter 3 One-electron atoms - the Scheoedinger equation for one-electron atoms - energy levels - the eigenfunctions of the bound states chapter 6 Two-electron atoms - the Scheoedinger equation for two-electron atoms - spin wave functions and the role of the Pauli exclusion principle - level scheme of two-electron atoms chapter 7 Many-electron atoms - the central field approximation - the periodic system of the elements chapter 9 Molecular structure - general nature of molecular structure - the Born-Oppenheimer separation for diatomic molecules - electronic structure of diatomic molecules - the structure of polyatomic molecules

N.W. Ashcroft, N.D, Mermin, “Solid State Physics”, Holt-Saunders Int. Ed. 1981
C. Kittel, “Introduction to Solid Sate Physics”, Wiley, 2004
 J. M. Ziman-Principles of the Theory of Solids - Cambridge University Press, 1979


Attendance to the lectures is not mandatory but strongly recommended.

There are two mid-term assessment tests during the course (lasting two hours each). If both tests are passed with a score of at least 15/30 and an average of not less than 18/30, the student is exempted from the written test for the entire academic year.
There are 5 complete calls (written and oral): two in the January/February session, two in the June/July session and one in the September session.
The written test (lasting three hours) includes two problems, each one divided into several questions. The written test is passed with a score of no less than 18/30 and is valid for the session in which it was taken.
The oral exam consists of an interview on the most relevant topics presented in the course. To pass the exam, the student must be able to present arguments and repeat calculations discussed and explained during the course. The student will be asked to apply the methods learned during the course to exercises or to examples and situations similar to those that were discussed in the course.
The evaluation takes into account:
- Correctness and completeness of the concepts discussed by the student;
- clarity and rigor of presentation;
- analytical development of the theory;
- problem-solving skills (method and results).

The final exam grade is determined by the average between the written score (or the average of the mid-term assessment tests) and the oral test score.

Crystal structures and Bravais lattice. Reciprocal lattice. Diffraction and solid crystals, structure factor. Electrons in solids, Bloch's theorem,. Band structure. Tightly and weakly bound electrons. Holes and effective mass. Born-Oppheneimer approximation. Lattice vibrations, phonons, specific heat (Einstein's and Debye's model, density of states). Electrons in metals and interaction with an electromagnetic field (metal transport properties): Drude's and Sommerfeld's models. The semiclassical model Intrinsic and extrinsic semiconductors. Temperature dependence of charge carrier density. Adopted texts N.W. Ashcroft, N.D, Mermin, `Solid State Physics', Holt-Saunders Int. Ed. 1981 C. Kittel, `Introduction to Solid Sate Physics', Wiley, 2004 J. M. Ziman, `Principles of the Theory of Solids', Cambridge University Press, 1979

The course relies on the following prerequisites: 1. CLASSICAL MECHANICS reference text: H. Goldstein, C. P. Poole, and J. L. Safko Classical Mechanics, Addison-Wesley chapter 1 Survey of elementary principles - mechanics of a particle - mechanics of a system of particles - contraints - D’Alambert’s principle and Lagrange’s equations chapter 6 Oscillations - formulation of the problem - the eigenvalue equation and the principal axis transformation - frequencies of free vibration and normal coordinates chapter 8 The Hamilton equations of motion - Legendre transformations and the Hamilton equations of motion chapter 9 Canonical transformations - the equations of canonical transformations - Poisson brackets - Liouville’s theorem 2. CLASSICAL ELECTROMAGNETISM reference text: D. Halliday, R. Resnick, and K. S. Crane Physics - part II, John Wiley & sons chapter 25 Electric charge and Coulomb’s law - electric charge - conductors and insulators - Coulomb’s law - continuous charge distributions - conservation of charge chapter 26 The electric field - the electric field - the electric field of point charges - the electric field of continuous charge distributions chapter 27 Gauss’ law - the flux of the electric field - Gauss’ law chapter 28 Electric potential energy and potential - electric potential energy - electric potential - calculating the potential from the field - potential due to point charges - potential due to continuous charge distributions - calculating the field from the potential - equipotential surfaces - the potential of a charged conductor chapter 29 The electric properties of materials - types of materials - a conductor in an alectric field - ohmic materials - Ohm’s law - an insultatori in an electric field chapter 30 Capacitance - capacitors - capacitance chapter 31 DC circuits - electric current - electromotive force chapter 32 The magnetic field - the magnetic force on a moving charge - circulating charges - the Hall effect 3. QUANTUM MECHANICS reference text: J. J. Sakurai Modern Quantum Mechanics, Addison-Wesley chapter 1 Fundamental concepts - kets, bras, operators - base kets and matrix representation - measurements, observables, and uncertainty relations - position, momentum, and translation - wave functions in position and momentum space chapter 2 Quantum dynamics - time evolution and the Shroedinger equation - the Shroedinger versus the Heisenberg picture - simple harmonic oscillator - Schroedinger’s wave equation chapter 3 Theory of angular momentum - rotations and angular momentum commutation relations - spin 1/2 systems and finite rotations - eigenvalues and eigenstates of angular momentum - orbital angular momentum - addition of angular momenta chapter 4 Symmetry in quantum mechanics - symmetries, conservation laws, and degeneracies - discrete symmetries, parity, or space inversion - lattice translation as a discrete symmetry - the time-reversal discrete symmetry chapter 5 Approximation methods - time independent perturbation theory: non degenerate case - time independent perturbation theory: the degenerate case 4. STATISTICAL MECHANICS reference text: K. Huang Statistical Mechanics, John Wiley & sons chapter 6 Classical statistical mechanics - the postulate of classical statistical mechanics - microcanonical ensemble - derivation of thermodynamics - equipartition theorem - classical ideal gas chapter 7 Canonical ensemble and grand canonical ensemble - canonical ensemble - energy fluctuations in the canonical ensemble - grand canonical ensemble - density fluctuations in the grand canonical ensemble - the chemical potential - equivalence of the canonical ensemble and grand canonical ensemble chapter 8 Quantum statistical mechanics - the postulate of quantum statistical mechanics - ensembles in quantum statistical mechanics - the ideal gases: micro canonical ensemble - the ideal gases: grand canonical ensemble chapter 11 Fermi systems - the equation of state of an ideal Fermi gas chapter 12 Bose systems - photons - Bose-Einstein condensation 5. ATOMIC AND MOLECULAR PHYSICS reference text: B. H Bransden & C. J. Joachain Physics of atoms and molecules, Longman Scientific & Technical chapter 3 One-electron atoms - the Scheoedinger equation for one-electron atoms - energy levels - the eigenfunctions of the bound states chapter 6 Two-electron atoms - the Scheoedinger equation for two-electron atoms - spin wave functions and the role of the Pauli exclusion principle - level scheme of two-electron atoms chapter 7 Many-electron atoms - the central field approximation - the periodic system of the elements chapter 9 Molecular structure - general nature of molecular structure - the Born-Oppenheimer separation for diatomic molecules - electronic structure of diatomic molecules - the structure of polyatomic molecules

N.W. Ashcroft, N.D, Mermin, “Solid State Physics”, Holt-Saunders Int. Ed. 1981
C. Kittel, “Introduction to Solid Sate Physics”, Wiley, 2004
 J. M. Ziman-Principles of the Theory of Solids - Cambridge University Press, 1979


Attendance to the lectures is not mandatory but strongly recommended.

There are two mid-term assessment tests during the course (lasting two hours each). If both tests are passed with a score of at least 15/30 and an average of not less than 18/30, the student is exempted from the written test for the entire academic year.
There are 5 complete calls (written and oral): two in the January/February session, two in the June/July session and one in the September session.
The written test (lasting three hours) includes two problems, each one divided into several questions. The written test is passed with a score of no less than 18/30 and is valid for the session in which it was taken.
The oral exam consists of an interview on the most relevant topics presented in the course. To pass the exam, the student must be able to present arguments and repeat calculations discussed and explained during the course. The student will be asked to apply the methods learned during the course to exercises or to examples and situations similar to those that were discussed in the course.
The evaluation takes into account:
- Correctness and completeness of the concepts discussed by the student;
- clarity and rigor of presentation;
- analytical development of the theory;
- problem-solving skills (method and results).

The final exam grade is determined by the average between the written score (or the average of the mid-term assessment tests) and the oral test score.