43006 - Physics of Matter (M-Z)

Learning outcomes

At the end of the class the student will have acquired knowledge about: a) the fundamental principles of statistical physics; b) the structure of atoms and molecules, as well as the basic notions of solid states.

Course contents

Module I semester

Recalls of Calculus of Probability: Axioms of probability and probability distributions. Examples (coin toss, random walk). Thermodynamic limit of the binomial distribution and Gaussian distribution. Central Limit Theorem. Introduction to the concept of microstate and macrostate. Boltzmann entropy.

Microcanonical ensemble: Introduction to statistical ensembles (microcanonical, canonical, grancanonical). Thermal contact and heat exchange. Principle of maximum entropy. Gibbs entropy. Examples and exercises.

Canonical ensamble: Partition function. Boltzmann distribution. Connections between statistics and thermodynamics. Examples and exercises.

The ideal gas: Distinguishable and indistinguishable particles. Monoatomic gas. Polyatomic gas (hints). Energy Equipartition Theorem. Examples and exercises.

Grancanonical ensemble: Concept of chemical potential. Partition functions. Chemical equilibrium and law of mass action. Examples and exercises.

Quantum statistical mechanics: Quantum particles, Bosons and Fermions. Maxwell-Boltzmann statistics. Fermi-Dirac distribution. Bose-Einstein distribution. Chemical potential of Fermions. Fermi energy. Examples and exercises.

Fermions and bosons: Thermal averaging, Sommerfeld expansion and thermodynamical properties of the Fermi. The Black Body. Bose-Einstein condensation (hints). Phonons. Examples and exercises.

Module II semester

Atomic Models: Atomic spectroscopy, Thomson’s model, Rutherford’s model, Bohr’s model, Franck-Hertz experiment, Sommerfeld model.

One-electron atom (H): The Schroedinger equation and its solution for the Hydrogen atom: energy levels and eigenfunctions of the bound states; radial distribution density. Orbital angular momentum and magnetic dipole moment; Stern-Gerlach experiment; Spin, Spin-orbit interaction. Dirac equation, perturbative solutions; Fine structure; Lamb shift and hyperfine structure. Selection rules and transition rates; Spectral line width and shapes.

Two-electron atom (He): The Schroedinger equation for two-electron atoms: ortho and para states. Spin wave functions and the Pauli exclusion principle. Energy level scheme for two-electron atoms. Ground state and excited states; Coulomb integral and exchange integral.

Many-electron atoms: The central field approximation; Hartree-Fock model and Slater determinants. The periodic table of the elements. X-ray spectra, Moseley’s law. Corrections to the central field approximation: L-S coupling and j-j coupling. Zeeman effect.

Molecules: Molecular structures. Ionic and covalent bond. The H2+ ion; Bonding and antibonding orbitals; Born-Oppenheimer approximation, LCAO method. Molecular roto-vibrational spectra (harmonic and anharmonic approximation).

Crystalline solids: Introduction to the band theory in solids; Crystalline and periodic structures; Bloch theorem, electrons in a solid; electron wave function in a lattice; Insulating, semiconducting and conducting materials.

Readings/Bibliography

Necessary Readings

Lecture notes and slides made available on Virtuale.unibo.it

Suggested Readings

Module I semester:

• Malcolm P. Kennett, Essential Statistical Physics,Cambridge University Press.
  
• Concepts in Thermal Physics, Stephen J. Blundell and Katherine M. Blundell, Oxford University Press.
  

Module II semester:

• B.H.Bransden & C.J. Joachain, Physics of Atoms and Molecules, ISBN-13: 978-0582356924.
• Eisberg-Resnick, Quantum Physics of Atoms, Molecules, Solids, Nuclei and Particles, Ed. Wiley ISBN-13: 978-0471873730.
  

Teaching methods

Frontal lectures and classroom tutorials for problem solving.

Assessment methods

The assessment test is the same for both modules and consists of two parts:

1. Written exam with 4 exercises (2 related to the content of the first-semester module and 2 related to the second-semester module). The score is out of 30 for each of the two modules, and the final grade will be calculated using a weighted average (0.4 for the first-semester module and 0.6 for the second-semester module).
   The written exam is passed only with a score equal to or greater than 18/30 and is valid only for the exam session in which it is passed.

2. Oral exam: the aim is to assess the student’s ability to understand, process, and analyze the course content.
   Grading scale for the final mark:

• Preparation on a very limited number of topics covered in the course and analytical skills that emerge only with the instructor’s help, overall correct use of language → 18–19;

• Preparation on a limited number of topics and autonomous analytical skills only on purely procedural matters, correct use of language → 20–24;

• Preparation on a broad range of course topics, ability to make independent critical analyses, command of specific terminology → 25–29;

• Comprehensive preparation on course topics, ability to make independent critical and interdisciplinary analyses, full command of specific terminology, and strong argumentation and self-reflection skills → 30–30L (30 with honors).
  As with the written part, the final oral exam grade will be calculated using the same weighted average of 0.4/0.6.

For attending students, it is possible to take a partial exam for the first-semester module (2 written exercises and a partial oral exam) only during the winter session (January and February exam dates), followed by the partial for the second-semester module (2 written exercises and a partial oral exam) only during the summer session (June and July exam dates).

Teaching tools

Frontal lecture at the blackboard, slides and projector.

Office hours

See the website of Domenico Di Sante

See the website of Cesare Franchini