Preliminaries on Quantization
By Elisa Ercolessi (U. Bologna)
September 1&2, 2014, IEMath, Granada (2+2 hours)
- Notes of the course.
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:
- The need of quantum mechanics: short history of the discovery of the physical phenomena that have led to a new theory;
- The general framework: the postulates of quantum mechanics and overview of the mathematical set-up; the geometric structure of the state of states.
- Realizations of the general framework: the Schrodinger and the Heisenberg picture; wave mechanics, coordinate and momentum representation, the canonical commutation relations, the Heisenberg principle;
- 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.