General Physics 3

The theory of relativity and quantum mechanics constitute the conceptual basis of the modern view of the physical world. Their knowledge has fundamentally changed both our representation of the world and the role we have in it. Since they concern the notions of space, time, interaction, and the intrinsic meaning of object and of physical law, these theories, should be a part, at least in their essential aspects, of the cultural heritage of every person interested in science. Moreover, their great formal and conceptual elegance is a prime example of the explanatory power of mathematics in physics.

The course, starting from the conceptual difficulties arising from the impossible coexistence of electromagnetism with classical mechanics, has as its objective the introduction to special relativity and quantum mechanics with special attention to their physical meaning and their vast conceptual implications. When appropriate and / or possible, experiments will also be made and the reading of famous passages taken from the literature will be done.
Few insights on some current problems in the physical research will also be provided.

Special Relativity: Maxwell's equations and their non-invariance under Galilean transformations. The vector potential. What is a physical law. Requests for invariance under the Euclidean and under the Galileo groups. The notions of space and time. Space-time.
The principle of relativity. Assumptions underlying the Lorentz transformations. Lorentz transformations. The relative nature of simultaneity. Length contraction and time dilation. Addition of velocities. Minkowski space-time. Scalar, contravariant and covariant vectors, controvariant and covariant tensors. Four-velocity and four-momentum, relativistic energy. First elements of relativistic dynamics: the four-force and four-acceleration. Relativistic Doppler effect and relativistic beaming. Relativistic formalism for electromagnetism.

Quantum mechanics
Some experimental results of matter optics. Scalar wave equation for matter beams. Non-relativistic approximation. Some experimental facts: quantized interaction. The Schrödinger equation. Einstein and de Broglie relations. Statistical interpretation of the wavefunction. Introduction of the notion of observable. Ehrenfest equation. Heisenberg's uncertainty relations. Applications of Schroedinger equation in one dimension. Finite dimensional quantum systems. States, observables and the general formalism of quantum mechanics.