Wednesday 19 December 2012 h. 15:00, room 2BC30

Daniele FONTANARI (Dip. Mat.)

"Geometric Quantization and Coherent States: a link between classical and quantum mechanics"

-Abstract

A physical system can be mathematically described either in the quantum or in the classical framework, the latter being an accurate approximation only when the magnitude of the physical quantities that characterize the system is large compared to the value of the Planck constant h. It is usually accepted that the "right" classical description of a system should emerge from the quantum one as a "limit for h close to 0". The inverse problem is also of great interest: given a classical description of a system, is it possible to find a suitable quantum one? Such a procedure, when properly defined, is called quantization.

In this talk I will give an introduction of the basic concepts and interpretations of (non-relativistic) Hamiltonian and quantum mechanics, then I will proceed with an overview of the apparatus of geometrical quantization. Finally, if time allows, I will show that coherent states naturally arise in the framework of geometric quantization and can be interpreted as quantum states that best approximate the classical ones.

The talk will be self-contained and no prior knowledge on classical mechanics, quantum mechanics or geometric quantization is required.

Rif. int. C. Marastoni, T. Vargiolu