34737 - Mathematical Foundations of Physics

Academic Year 2026/2027

  • Teaching Mode: In-person learning (entirely or partially)
  • Campus: Bologna
  • Corso: Second cycle degree programme (LM) in Mathematics (cod. 6730)

Learning outcomes

At the end of the course, the student has an exact knowledge of the mathematical formalisms underlying physical theories. In particular, it focus on those parts of mathematics developed for the comprehension of some physical phenomena. Better understands of physics better through depth knowledge of its mathematical language.

Course contents

Special Relativity

- Wave equation, decomposition into plane waves, waves and the principle of relativity.

- Absolute motion, aether theory, Lorentz theory: from the experiments to Einstein's theory;

- Relativistic Kinematics: Lorentz transformations, relativistic composition of velocities, simultaneity and causality, Minkowski spacetime;

- Relativistic Dynamics: principle of relativity and relativistic mass; mass–energy equivalence; four-momentum and conservation laws; decays, disintegrations, and binding energy.

 

Principles of Quantum Mechanics

- Emission and absorption spectra, Planck’s law, and the photoelectric effect;

- From atomic models to Bohr–Sommerfeld quantization;

- Introduction to the Schrödinger equation: geometrical and wave optics, classical and wave mechanics, and de Broglie theory;

- Axioms of Quantum Mechanics and their connection with the theory of linear operators in Hilbert spaces.

 

Readings/Bibliography

Class notes

 

Teta, Alessandro. A Mathematical Primer on Quantum Mechanics. Berlin: Springer, 2018.

Teaching methods

Classroom lectures

Assessment methods

The exam consists of an oral interview in order to verify the knowledge of the arguments listed in the Course Contents. The oral exam starts with a question on a subject chosen by the student.

Teaching tools

Lecture notes and updated record of lessons.

Office hours

See the website of Daniele Tantari