67114 - Structure of Matter

Learning outcomes

In this course, the student gains knowledge about: a) the physics of quantum states, in particular electron states, in systems of increasing complexity from hydrogenic atoms to crystalline solids; b) the interactions of these systems with electromagnetic radiation; c) the importance of such interactions for astronomical observations. The student becomes able to apply quantum mechanical principles and methods to calculate energy levels, perturbations, and transition rates. Moreover, he/she learns how to calculate the properties of radiative transitions relevant for astronomical studies, such as energy, lifetime and natural width.

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 magnetic fields: Zeeman effect
• Many electrons atoms
  • Indistinguishable particles in quantum mechanics: fermions and bosons
  • Two-electron atoms: exchange interaction
  • Central field approximation: configurations and subshells
    
  • 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
  • The optical spectra of the alkali
  • Examples in astronomy, Grotrian diagrams
  • X-ray spectra and Moseley's law
• 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
  • 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
• 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
• Optical properties of solids
  • Optical materials
  • Interband absorption
  • Luminescence

 

Readings/Bibliography

IMPORTANT: A BASIC KNOWLEDGE OF QUANTUM MECHANICS IS ABSOLUTELY NECESSARY IN ORDER TO FOLLOW THE COURSE!

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ATOMIC AND MOLECULAR PHYSICS

•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

PHYSICS OF SOLIDS

•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 when necessary

Exercises (both within lectures and assigned as homework)

Occasional use of anonymous quiz with the Wooclap platform

Assessment methods

Exam Assessment

The exam consists of a written test and an oral exam, organized as follows:

1) Written test
The written exam includes two or three exercises, each composed of multiple sub-questions.

• The exercises are similar to those covered during lectures and collected in the problem set available on Virtuale.

• The use of books, notes, formula sheets, and calculators is permitted (smartphones are not allowed).

• Examples of past exams with solutions are available on Virtuale.

• Two midterm exams will be held during the course (during lecture hours), in addition to five scheduled exams throughout the rest of the academic year.

• The score for the written test ranges from 1 to 30.

To access the oral exam, the student must pass the written test with a score of 18/30 or higher. If the student takes both midterms, the average of the two grades is used (it is not necessary to obtain at least 18 in each individual midterm).

2) Oral exam

• First topic: chosen by the student from the list of topics covered in the course. The presentation can be given using PowerPoint or PDF format (15 minutes + 5–10 minutes for discussion). Optional in-depth exploration or development of computational or visualization tools relevant to the topic is welcome but not required.

• Second topic: randomly selected from a list available on Virtuale. Detailed derivations are not required for this second topic, but students should provide a clear explanation of the key points and the relevant physical concepts.

Oral exam grading criteria:

• 29–30L: Comprehensive understanding of all topics, strong analytical skills, and mastery of technical terminology

• 26–28: Strong preparation on the chosen topic and fair to good understanding of the second topic, critical thinking ability, proper use of terminology and language

• 22–25: Good preparation on the chosen topic and fair knowledge of the second, analytical thinking that emerges with guidance, generally correct language

• 18–21: Fair preparation on the chosen topic and sufficient knowledge of the second, analytical thinking that emerges only with guidance, overall acceptable language

Final grade:
The final grade is typically the arithmetic average of the written and oral exam scores (provided the oral exam is passed). Up to two additional points may be awarded if the oral performance is particularly strong.

If the oral exam is not passed, it must be retaken during a future session. The written exam result remains valid only for the current academic year.

The grade obtained following the oral exam may be rejected a maximum of two times, as decided by the Degree Programme Board.

Students with Specific Learning Disorders (SLD) or temporary/permanent disabilities are strongly advised to contact the University's dedicated office in advance (https://site.unibo.it/studenti-con-disabilita-e-dsa/en ). This office will be responsible for proposing any necessary accommodations to the interested students. Such accommodations must be submitted to the instructor for approval at least 15 days in advance, and will be assessed in relation to the learning objectives of the course.

Teaching tools

The recorded lectures are available on Virtuale until the end of the course.

Selected numerical examples in MATLAB

Questionnaires on the Wooclap platform are available in asynchronous mode to summarize and reflect on the main concepts of each chapter.

Office hours

See the website of Luca Pasquini