Basic quantisation rules of semiclassical analysis

Semiclassical analysis is the study of how to connect classical mechanics with quantummechanics in a mathematically rigorous way. What is crucial for quantum mechanics isthat the operators that occur are self-adjoint and map a subset of L2 into L2. This hasbeen proven in this thesis. Also, a technique of asymptotic expansion of functions interms of Planck's constant h is developed, in order to study the so called semiclassicallimit (i.e. the limit as h approaches 0) We also develop different approaches toquantisation, and a calculus of operators (i.e. quantum observables) based on acalculus for their corresponding symbols (or classical observables)