Preliminaries on Quantization

By Elisa Ercolessi (U. Bologna)

September 1&2, 2014, IEMath, Granada (2+2 hours)

This is a pre-course on basic elements required for the course Methods on Quantization. If you are interested in this pre-course, please, send us an e-mail to xxiiifwgp[ at ]gmail.com in order to organize it conveniently.

The goal of this pre-course is to introduce the basic tools of quantum mechanics, necessary to understand the different techniques of quantization.

The topics of the two lectures will cover:

  1. The need of quantum mechanics: short history of the discovery of  the physical phenomena that have led to a new theory;
  2. The general framework: the postulates of quantum mechanics and overview of the mathematical set-up; the geometric structure of the state of states.
  3. Realizations of the general framework: the Schrodinger and  the Heisenberg picture; wave mechanics,  coordinate and momentum representation, the canonical commutation relations, the Heisenberg principle;
  4. Key examples: free particle in coordinate and momentum representation; the harmonic oscillator, bosonic creation/annihilation operators; spin and two level systems, fermionic creation/annihilation operators.