#
Structure of Matter 1

A.Y. 2021/2022

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

Course syllabus and organization

### CORSO A

Responsible

Lesson period

Second semester

More specific information on the delivery modes of training activities for academic year 2021122 will be provided over the coming months, based on the evolution of the public health situation.

**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://sites.google.com/site/strutturadellamateriacorsoa

WEB PAGE OF THE COURSE: https://sites.google.com/site/strutturadellamateriacorsoa

**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://labonline.ctu.unimi.it/course/view.php?id=43

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://labonline.ctu.unimi.it/course/view.php?id=43

**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

eaching:

In case of travel restrictions due to Covid-19, the course will be fully delivered through remote teaching.

In this case, the lectures will be offered in virtual classrooms (zoom platform) in synchronous connection, with the possibility of real-time interaction between the students and the teacher.

Support material:

The program and supporting material remain the same.

Final tests:

Written tests, in case of travel restrictions due to Covid-19, are carried out over a teleconferencing platform. Students are asked to prove verbally that they are capable to solve problems analogous to those of regular written tests.

In case of travel restrictions due to Covid-19, oral tests are carried out over a teleconferencing platform. The teacher transmits the connection instruction to the booked students.

In case of travel restrictions due to Covid-19, the course will be fully delivered through remote teaching.

In this case, the lectures will be offered in virtual classrooms (zoom platform) in synchronous connection, with the possibility of real-time interaction between the students and the teacher.

Support material:

The program and supporting material remain the same.

Final tests:

Written tests, in case of travel restrictions due to Covid-19, are carried out over a teleconferencing platform. Students are asked to prove verbally that they are capable to solve problems analogous to those of regular written tests.

In case of travel restrictions due to Covid-19, oral tests are carried out over a teleconferencing platform. The teacher transmits the connection instruction to the booked students.

**Course syllabus**

The course targets a basic microscopic understanding of many fundamental phenomena regarding matter in its atomic, molecular and solid states. Spectroscopy data are discussed in terms of basic quantum mechanics. Elements of equilibrium and transport statistics complete the phenomenological/conceptual picture.

Detailed program:

Introductory Concepts: basic Ingredients and typical scales.

Spectra and broadening.

I. ATOMIC PHYSICS

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 and Fine Structure;

Nuclear Spin and Hyperfine Structure;

Electronic Transitions, Selection Rules;

Spectra in a Magnetic Field.

Many-Electron Atoms: Identical Particles;

The Independent-Particles Approximation;

The 2-Electron Atom; The Hartree-Fock Method;

Electronic Structure Across the Periodic Table;

Fundamentals of Spectroscopy;

Core Levels and Spectra; Optical Spectra;

Electric-dipole Selection Rules.

II. MOLECULAR PHYSICS

The Adiabatic Separation.

Chemical and Non-chemical Bonding:

The Molecular Ion H2+; Covalent and Ionic Bonding;

Weak Non-chemical Bonds; Classification of Bonding.

Intramolecular Dynamics and Spectra:

Rotational and Rovibrational Spectra;

Electronic Excitations; Zero-Point Effects.

III. STATISTICAL PHYSICS

Introductory Concepts:

Probability and Statistics;

Quantum Statistics and the Density Operator.

Equilibrium Ensembles:

Connection to Thermodynamics;

Entropy and the Second Principle.

Ideal Systems:

The high-temperature gas;

Low-temperature Fermi and Bose Gases.

Interaction Matter-Radiation, the Laser

IV. SOLIDS

The microscopic structure of solids: lattices and crystal structures;

The reciprocal lattice and diffraction experiments.

Electrons in crystals: Bloch's theorem and models of electronic bands in crystals;

Filling of the bands: metals and insulators; effective mass.

Semiconductors: valence and conduction bands;

Spectra of electrons in solids.

-Atomic motions in a crystalline solid: the 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; the Debye model.

Other phonon effects.

Detailed program:

Introductory Concepts: basic Ingredients and typical scales.

Spectra and broadening.

I. ATOMIC PHYSICS

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 and Fine Structure;

Nuclear Spin and Hyperfine Structure;

Electronic Transitions, Selection Rules;

Spectra in a Magnetic Field.

Many-Electron Atoms: Identical Particles;

The Independent-Particles Approximation;

The 2-Electron Atom; The Hartree-Fock Method;

Electronic Structure Across the Periodic Table;

Fundamentals of Spectroscopy;

Core Levels and Spectra; Optical Spectra;

Electric-dipole Selection Rules.

II. MOLECULAR PHYSICS

The Adiabatic Separation.

Chemical and Non-chemical Bonding:

The Molecular Ion H2+; Covalent and Ionic Bonding;

Weak Non-chemical Bonds; Classification of Bonding.

Intramolecular Dynamics and Spectra:

Rotational and Rovibrational Spectra;

Electronic Excitations; Zero-Point Effects.

III. STATISTICAL PHYSICS

Introductory Concepts:

Probability and Statistics;

Quantum Statistics and the Density Operator.

Equilibrium Ensembles:

Connection to Thermodynamics;

Entropy and the Second Principle.

Ideal Systems:

The high-temperature gas;

Low-temperature Fermi and Bose Gases.

Interaction Matter-Radiation, the Laser

IV. SOLIDS

The microscopic structure of solids: lattices and crystal structures;

The reciprocal lattice and diffraction experiments.

Electrons in crystals: Bloch's theorem and models of electronic bands in crystals;

Filling of the bands: metals and insulators; effective mass.

Semiconductors: valence and conduction bands;

Spectra of electrons in solids.

-Atomic motions in a crystalline solid: the 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; the Debye model.

Other phonon effects.

**Prerequisites for admission**

Basic electromagnetism: electric field and potential, magnetic fields, Lorentz force dipole-field interaction. Oscillating fields: electromagnetic waves, polarization, basic wave optics (interference/diffraction).

Basic special relativity: energy-momentum 4-vector.

Elements of quantum mechanics (wave equation in 1 dimension, stationary states uncertainty principle, tunneling, elementary 1D problems).

Basic special relativity: energy-momentum 4-vector.

Elements of quantum mechanics (wave equation in 1 dimension, stationary states uncertainty principle, tunneling, elementary 1D problems).

**Teaching methods**

The course alternates lectures, where topics are presented from a theoretical and phenomenological point of view, with practicals, with the same topic covered through numerical problem solution at the blackboard. In the problem-solving section the addressed problems are similar to those of the written test.

**Teaching Resources**

N. Manini, Introduction to the Physics of Matter - Basic Atomic, Molecular, and Solid-State Physics, 2nd ed. (Springer, 2020).

A. Rigamonti, P. Carretta, Structure of matter. An introductory course with problems and solutions (Springer, 2009).

R. Eisberg and R. Resnick, Quantum Physics 2nd ed. (Wiley, 1974).

J.J. Brehm and W.J. Mullin, Introduction to the Structure of Matter (Wiley, 1989).

Course web page: http://materia.fisica.unimi.it/manini/dida/Struttura_della_Materia_1.html

A. Rigamonti, P. Carretta, Structure of matter. An introductory course with problems and solutions (Springer, 2009).

R. Eisberg and R. Resnick, Quantum Physics 2nd ed. (Wiley, 1974).

J.J. Brehm and W.J. Mullin, Introduction to the Structure of Matter (Wiley, 1989).

Course web page: http://materia.fisica.unimi.it/manini/dida/Struttura_della_Materia_1.html

**Assessment methods and Criteria**

Written test and oral test.

The written test consists of 4 problems, to be solve in 3 hours.

http://materia.fisica.unimi.it/manini/dida/archive.exam.html reports problems from previous tests.

The correct solution of 2 problems guarantees the access to the oral test. For the final grade, the correct solution of 3 problems adds 1 bonus point to the oral-test grade; the correct solution of 4 problems adds 2 bonus points to the oral-test grade.

The oral test has typical duration of 1 hour. It consists in questions and short problems aiming to gauge the depth of understanding of the course topics and a clear feeling of the correct orders of magnitude of the involved quantities.

The written test consists of 4 problems, to be solve in 3 hours.

http://materia.fisica.unimi.it/manini/dida/archive.exam.html reports problems from previous tests.

The correct solution of 2 problems guarantees the access to the oral test. For the final grade, the correct solution of 3 problems adds 1 bonus point to the oral-test grade; the correct solution of 4 problems adds 2 bonus points to the oral-test grade.

The oral test has typical duration of 1 hour. It consists in questions and short problems aiming to gauge the depth of understanding of the course topics and a clear feeling of the correct orders of magnitude of the involved quantities.

FIS/03 - PHYSICS OF MATTER - University credits: 9

Practicals: 48 hours

Lessons: 40 hours

Lessons: 40 hours

Professors:
Di Vece Marcel, Manini Nicola

Educational website(s)

Professor(s)

Reception:

Wednesday afternoon, better by e-mail appointment

Via Celoria 16, LITA Building, ground floor (Latitude 45.47606 N Longitude 9.23026 E)