Structure of Matter 1
A.Y. 2024/2025
Learning objectives
The purpose of the course is covering the basic microscopic and spectroscopic properties of matter, in its atomic, molecular and crystalline states.
Expected learning outcomes
At the end of the course, the student is expected to master the following competences and skills:
1. The basics of the radiation-matter interaction in the electric dipole approximation (selection rules for atomic transitions). Distinguish and understand emission and absorption experiments.
2. A working knowledge and understanding of the 1-electron atom/ions spectroscopy: line series, relativistic effects, dependence on the nuclear charge Z, atomic angular momentum, interaction with a static magnetic field, associated typical time- and energy-scales.
3. Basic understanding of the spectroscopy of the many-electron atoms/ions. Appreciate the nature of the core and optical transitions, particularly in alkali atoms. Appreciate the difficulties relative to incomplete atomic shells, and become capable to evaluate the basic properties of the atomic ground state.
4. A clear picture of the adiabatic separation between the nuclear and the electronic motions.
5. Understand the different origins of the molecular bond.
6. Distinguish and interpret the spectra of the diatomic molecules.
7. A deep understanding of the microscopic significance of temperature (canonical ensemble). Interpret correctly the Boltzmann statistics of simple ideal systems (diatomic molecular gases, spin systems.
8. Understand the free-fermion model for the electrons in matter: Pauli principle, Fermi energy, phenomenology of electrons in metals (heat capacity and magnetic susceptibility).
9. Command a working interpretation of the radiation spectra emitted by hot objects in terms of photon statistics. Discuss the spectroscopy experiments in terms of spontaneous/stimulated emission and absorption rates.
10. Get acquainted with a few typical structures of crystalline solids, understand the basic principles guiding their formation in several common materials.
11. Understand the concept of electronic bands in crystalline solids, their relevance for the transport and spectroscopic properties of metals and semiconductors.
1. The basics of the radiation-matter interaction in the electric dipole approximation (selection rules for atomic transitions). Distinguish and understand emission and absorption experiments.
2. A working knowledge and understanding of the 1-electron atom/ions spectroscopy: line series, relativistic effects, dependence on the nuclear charge Z, atomic angular momentum, interaction with a static magnetic field, associated typical time- and energy-scales.
3. Basic understanding of the spectroscopy of the many-electron atoms/ions. Appreciate the nature of the core and optical transitions, particularly in alkali atoms. Appreciate the difficulties relative to incomplete atomic shells, and become capable to evaluate the basic properties of the atomic ground state.
4. A clear picture of the adiabatic separation between the nuclear and the electronic motions.
5. Understand the different origins of the molecular bond.
6. Distinguish and interpret the spectra of the diatomic molecules.
7. A deep understanding of the microscopic significance of temperature (canonical ensemble). Interpret correctly the Boltzmann statistics of simple ideal systems (diatomic molecular gases, spin systems.
8. Understand the free-fermion model for the electrons in matter: Pauli principle, Fermi energy, phenomenology of electrons in metals (heat capacity and magnetic susceptibility).
9. Command a working interpretation of the radiation spectra emitted by hot objects in terms of photon statistics. Discuss the spectroscopy experiments in terms of spontaneous/stimulated emission and absorption rates.
10. Get acquainted with a few typical structures of crystalline solids, understand the basic principles guiding their formation in several common materials.
11. Understand the concept of electronic bands in crystalline solids, their relevance for the transport and spectroscopic properties of metals and semiconductors.
Lesson period: Activity scheduled over several sessions (see Course syllabus and organization section for more detailed information).
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course cannot be attended as a single course. Please check our list of single courses to find the ones available for enrolment.
Course syllabus and organization
CORSO A
Responsible
Lesson period
Second semester
Course syllabus
The course aims to develop the basic microscopic understanding of many fundamental phenomena concerning matter in its atomic, molecular and solid states. Atomic, molecular and crystal spectroscopy data are discussed, based on notions of elementary quantum mechanics. Elements of equilibrium and transport statistics in solids complete the phenomenological / interpretative framework. The detailed program is as follows:
I. Atomic physics:
Line width. Doppler, extrinsic, and intrinsic broadening;
One-Electron Atom/Ions: The Energy Spectrum;
The Angular and Radial Wavefunctions;
Orbital Angular Momentum and Magnetic Dipole Moment;
The Stern-Gerlach Experiment;
Electron Spin, spin magnetic moment, spin-orbit interaction, fine structure effects;
Relativistic correction to the kinetic energy;
Nuclear Spin and Hyperfine Structure;
Electronic Transitions, Dipole Selection Rules, and transition probabilities;
Many-Electron Atoms: Identical Particles;
The Independent-Particles Approximation;
The 2-Electron Atom; Singlet and Triplet states, Slater Determinants;
The Hartree-Fock Method: effective self-consistent Hamiltonian;
Electronic Structure Across the Periodic Table, L-S (Russel-Saunders) coupling, Hund's rules;
Electronic transitions and Dipole selection rules in many-electrons atoms;
Fundamentals of Spectroscopy; optical spectra, case of alkali atoms;
Core-Levels and X-Ray emission spectra, X-Ray absorption threshold.
II. Elements of molecular physics:
- The adiabatic approximation;
H2+ and H2 molecules, Atomic orbitals method;
Hybridization of orbitals and directional bonds (outline);
Intramolecular dynamics, Rotational and Vibrational molecular states and their spectra;
Electronic excitations and Franck-Condon principle;
Zero-point effects.
III. Elements of quantum statistical mechanics:
- Macroscopic system and statistical description. Probability of microstates and Gibbs distribution, thermodynamic equilibrium ensembles, microscopic significance of temperature and entropy (outline);
- Ideal systems of non-interacting particles:
- Independent and distinguishable particles: non-degenerate limit (high temperture-low density- large mass limit); Maxwell-Boltzmann distribution. Applications: ideal monoatomic gas, two-level system and paramagnetism, specific heat of a gas of diatomic molecules;
- Indistinguishable non-interacting fermions: Fermi-Dirac distribution. Low temperature Fermi gas: energy, temperature and Fermi moment. Applications: specific heat and paramagnetism of electrons in metals;
- Indistinguishable non-interacting bosons: Bose-Einstein distribution (outline). Applications: photon "gas" and Planck's law;
- Radiation-matter interaction: absorption, spontaneous emission and stimulated emission. Einstein relations. Population inversion and radiation amplification. Scheme of operation of a laser (outline).
IV. Elements of physics of solids:
- Structure of crystalline solids. The direct lattice and the reciprocal lattice. Diffraction experiments;
- Electronic states in solids, Bloch's Theorem and energy bands. Almost free electrons and the formation of energy gaps. Filling of the bands: metals and insulators.
-Extraction potential. Electron dynamics in semiclassical approximation. Effective mass;
-Electron scattering by defects and phonons: electrical resistivity;
-Specific heat of metals;
-Semiconductors: valence and conduction bands;
- Atomic motions in a crystalline solid: harmonic approximation, normal modes of vibration, and phonons. Phonon dispersion curve for a one-dimensional chain: acoustic and optical modes. Phonons in 3 dimensions: longitudinal and transverse modes. Phonon "gas", specific heat of solids, Debye model.
I. Atomic physics:
Line width. Doppler, extrinsic, and intrinsic broadening;
One-Electron Atom/Ions: The Energy Spectrum;
The Angular and Radial Wavefunctions;
Orbital Angular Momentum and Magnetic Dipole Moment;
The Stern-Gerlach Experiment;
Electron Spin, spin magnetic moment, spin-orbit interaction, fine structure effects;
Relativistic correction to the kinetic energy;
Nuclear Spin and Hyperfine Structure;
Electronic Transitions, Dipole Selection Rules, and transition probabilities;
Many-Electron Atoms: Identical Particles;
The Independent-Particles Approximation;
The 2-Electron Atom; Singlet and Triplet states, Slater Determinants;
The Hartree-Fock Method: effective self-consistent Hamiltonian;
Electronic Structure Across the Periodic Table, L-S (Russel-Saunders) coupling, Hund's rules;
Electronic transitions and Dipole selection rules in many-electrons atoms;
Fundamentals of Spectroscopy; optical spectra, case of alkali atoms;
Core-Levels and X-Ray emission spectra, X-Ray absorption threshold.
II. Elements of molecular physics:
- The adiabatic approximation;
H2+ and H2 molecules, Atomic orbitals method;
Hybridization of orbitals and directional bonds (outline);
Intramolecular dynamics, Rotational and Vibrational molecular states and their spectra;
Electronic excitations and Franck-Condon principle;
Zero-point effects.
III. Elements of quantum statistical mechanics:
- Macroscopic system and statistical description. Probability of microstates and Gibbs distribution, thermodynamic equilibrium ensembles, microscopic significance of temperature and entropy (outline);
- Ideal systems of non-interacting particles:
- Independent and distinguishable particles: non-degenerate limit (high temperture-low density- large mass limit); Maxwell-Boltzmann distribution. Applications: ideal monoatomic gas, two-level system and paramagnetism, specific heat of a gas of diatomic molecules;
- Indistinguishable non-interacting fermions: Fermi-Dirac distribution. Low temperature Fermi gas: energy, temperature and Fermi moment. Applications: specific heat and paramagnetism of electrons in metals;
- Indistinguishable non-interacting bosons: Bose-Einstein distribution (outline). Applications: photon "gas" and Planck's law;
- Radiation-matter interaction: absorption, spontaneous emission and stimulated emission. Einstein relations. Population inversion and radiation amplification. Scheme of operation of a laser (outline).
IV. Elements of physics of solids:
- Structure of crystalline solids. The direct lattice and the reciprocal lattice. Diffraction experiments;
- Electronic states in solids, Bloch's Theorem and energy bands. Almost free electrons and the formation of energy gaps. Filling of the bands: metals and insulators.
-Extraction potential. Electron dynamics in semiclassical approximation. Effective mass;
-Electron scattering by defects and phonons: electrical resistivity;
-Specific heat of metals;
-Semiconductors: valence and conduction bands;
- Atomic motions in a crystalline solid: harmonic approximation, normal modes of vibration, and phonons. Phonon dispersion curve for a one-dimensional chain: acoustic and optical modes. Phonons in 3 dimensions: longitudinal and transverse modes. Phonon "gas", specific heat of solids, Debye model.
Prerequisites for admission
1) Classical Newtonian and Hamiltonian mechanics.
2) Basic thermodynamics (internal energy, free energy, entropy).
3) Elements of "static" electromagnetism (electric field, electric potential, magnetic field, Lorenz force, field-dipole interaction) and of electromagnetism of oscillating fields: electromagnetic waves, polarization, basic concepts of wave optics (interference / diffraction).
4) Elements of relativistic mechanics, energy-impulse quadrivector.
5) Heisenberg's uncertainty principle.
6) Elements of wave mechanics, De Broglie wavelength.
7) The time-dependent Schroedinger equation.
8) The time-independent Schroedinger's equation: stationary states, eigenvalues and eigenfunctions.
9) Elementary problems involving the calculation of eigenvalues and eigenfunctions in quantum mechanics, e.g. the infinite flat potential hole, and the 1-dimensional harmonic oscillator.
10) Elements of analog electronics: Ohm's law and I-V characteristic of a passive component.
2) Basic thermodynamics (internal energy, free energy, entropy).
3) Elements of "static" electromagnetism (electric field, electric potential, magnetic field, Lorenz force, field-dipole interaction) and of electromagnetism of oscillating fields: electromagnetic waves, polarization, basic concepts of wave optics (interference / diffraction).
4) Elements of relativistic mechanics, energy-impulse quadrivector.
5) Heisenberg's uncertainty principle.
6) Elements of wave mechanics, De Broglie wavelength.
7) The time-dependent Schroedinger equation.
8) The time-independent Schroedinger's equation: stationary states, eigenvalues and eigenfunctions.
9) Elementary problems involving the calculation of eigenvalues and eigenfunctions in quantum mechanics, e.g. the infinite flat potential hole, and the 1-dimensional harmonic oscillator.
10) Elements of analog electronics: Ohm's law and I-V characteristic of a passive component.
Teaching methods
Teaching is provided in a traditional way, with frontal lectures and exercises. Each lesson typically lasts 2 hours, with an interval of 10-15 minutes after the first part. Intensive use of the blackboard is made, with projection of some slides in support, if deemed useful. The teacher also provides online material for further information and for some details of calculations that would require excessive time if done entirely in class. Attendance is mandatory.
WEB PAGE OF THE COURSE: https://labonline.ctu.unimi.it/course/view.php?id=43
WEB PAGE OF THE COURSE: https://labonline.ctu.unimi.it/course/view.php?id=43
Teaching Resources
Textbooks:
1) N. Manini, Introduction to the Physics of Matter - Basic Atomic,
Molecular, and Solid-State Physics, 2nd ed. (Springer, 2020)
2) A. Rigamonti, P. Carretta, Structure of matter. An introductory course with problems and solutions (Springer, 2009).
3) R. Eisberg and R. Resnick, Quantum Physics 2nd ed. (Wiley, 1974).
4) J.J. Brehm and W.J. Mullin, Introduction to the Structure of Matter (Wiley, 1989)
WEB PAGE OF THE COURSE: https://myariel.unimi.it/course/view.php?id=47
1) N. Manini, Introduction to the Physics of Matter - Basic Atomic,
Molecular, and Solid-State Physics, 2nd ed. (Springer, 2020)
2) A. Rigamonti, P. Carretta, Structure of matter. An introductory course with problems and solutions (Springer, 2009).
3) R. Eisberg and R. Resnick, Quantum Physics 2nd ed. (Wiley, 1974).
4) J.J. Brehm and W.J. Mullin, Introduction to the Structure of Matter (Wiley, 1989)
WEB PAGE OF THE COURSE: https://myariel.unimi.it/course/view.php?id=47
Assessment methods and Criteria
The written test includes the solution of exercises, similar to those presented in class.
The written test is particularly important, as it allows to verify, among other things, that students have acquired a correct knowledge about orders of magnitude of the calculated quantities, often far from our direct experience. Written tests since 2001 are available at the URL http://materia.fisica.unimi.it/manini/dida/archive.exam.html
The oral exam consists of a discussion that focuses on topics covered in the course and / or on the written test, and has a duration ranging from about 30 to about 60 minutes.
The evaluation criteria take into account both the written and the oral test (correctness of the answers, clarity of exposition, ability to synthesize). Following the oral exam, the final mark can vary on the whole spectrum of the score.
The written test is particularly important, as it allows to verify, among other things, that students have acquired a correct knowledge about orders of magnitude of the calculated quantities, often far from our direct experience. Written tests since 2001 are available at the URL http://materia.fisica.unimi.it/manini/dida/archive.exam.html
The oral exam consists of a discussion that focuses on topics covered in the course and / or on the written test, and has a duration ranging from about 30 to about 60 minutes.
The evaluation criteria take into account both the written and the oral test (correctness of the answers, clarity of exposition, ability to synthesize). Following the oral exam, the final mark can vary on the whole spectrum of the score.
FIS/03 - PHYSICS OF MATTER - University credits: 9
Practicals: 48 hours
Lessons: 40 hours
Lessons: 40 hours
Professors:
Guerra Roberto, Onida Giovanni
CORSO B
Responsible
Lesson period
First semester
FIS/03 - PHYSICS OF MATTER - University credits: 9
Practicals: 48 hours
Lessons: 40 hours
Lessons: 40 hours
Professors:
Di Vece Marcel, Manini Nicola
Professor(s)
Reception:
Tuesdays 2pm - 5pm
office, Via Celoria 16, LITA building, room A/T/C11
Reception:
Wednesday afternoon, better by e-mail appointment
Via Celoria 16, LITA Building, ground floor (Latitude 45.47606 N Longitude 9.23026 E)