67114 - Structure of Matter

Course Unit Page


This teaching activity contributes to the achievement of the Sustainable Development Goals of the UN 2030 Agenda.

Quality education

Academic Year 2021/2022

Learning outcomes

At the end of the course, the student knows the fundamental physics that govern the structure and properties of atoms and molecules as well as their interaction with electromagnetic radiation.  He/she will learn how to apply quantum mechanics to calculate quantities like transition probabilities, interaction energies, ground state and excited state energies. Moreover, he/she will be able to predict and understand the optical spectra of atoms and simple molecules that are relevant in astronomy and astrophysics.


Course contents


  • The hydrogenic atoms
    • Wave functions and energy levels
  • Interaction of hydrogenic atoms with the electromagnetic radiation
    • Transition probabilities
    • Dipole approximation
    • Einstein coefficients
    • Selection rules and optical spectra
    • Scattering of radiation
  • Fine and hyperfine structure of hydrogenic atoms
    • Spin and magnetic moment
    • Spin-orbit coupling
    • Hyperfine structure
    • External static fields: Stark and Zeeman effect
  • Many electrons atoms
    • Indistinguishable particles in quantum mechanics: fermions and bosons
    • Two-electron atoms: exchange interaction
    • Central field approximation: configurations and subshells
    • Hartree-Fock methods
    • Corrections to the central field approximation: correlation effects: L-S coupling and JJ coupling
  • Interaction of many electron atoms with electromagnetic radiation
    • Selection rules for E1, M1, E2 transitions
    • Optical spectra of the alkali
    • Examples in astronomy, Grotrian diagrams
    • X-ray spectra
  • Molecules: quantum states and interaction with electromagnetic radiation
    • Born-Oppenheimer approximation
    • Electronic structure and symmetry of diatomic molecules
    • The H2+ molecular ion and LCAO method
    • The H2 molecule, covalent bonding
    • Molecular orbitals
    • Polyatomic molecules: hybridization, delocalized orbitals
    • Molecular spectra: rotational-roto-vibrational, and electronic


  • Introduction to the solid state
    • Crystalline versus amorphous solids
    • Solids in the interstellar medium
  • Structure of crystals
    • Periodic lattices
    • X-ray and electron diffraction
    • Lattice vibrations: phonons
  • Electron states in solids
    • Free electron model of metals
    • Bloch states for electrons in a periodic potential
    • Tight binding model of electrons in solids
    • Energy bands and forbidden gap
    • Conductors vs insulators
    • Electrons and holes in semiconductors
  • Optical properties of solids
    • Optical materials
    • Interband absorption
    • Luminescence
    • Point defects and solid-state lasers
    • Optical properties of metals; plasmons




•B.H. Bransden & C.J. Joachain, Physics of Atoms and Molecules, Prentice Hall, 2° Edition 2003

•R. Eisberg, R, Resnick, Qantum Physics of Atoms, Molecules, Solids, Nuclei and Particles, Wiley

•J. Tennyson, Astronomical Spectroscopy, Imperial College Press


•C. Kittel, Introduction to Solid State Physics, Wiley

•M. Fox, Optical properties of solids, Oxford University Press

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Slides used during the lectures

Specific notes for selected calculations

MATLAB scripts

Teaching methods

Frontal lectures with video-projection of slides in blended synchronized mode, i.e. both in the classroom and online via MS Teams.

Exercises (both within lectures and assigned as homework)

Selected topic will be treated in "peer instruction" mode

Assessment methods

Written and oral examination:

1) written examination: solution of simple exercises

2) oral examination: first part on a course topic chosen by the student, second part on an argument selected by the teacher

Teaching tools

Microsoft Teams for online lectures

Selected examples in MATLAB

Wooclap for discussions and polls for each chapter and for topics assigned in "peer instruction" mode

Office hours

See the website of Luca Pasquini