Introduction to Mathematical Physics/Quantum mechanics/Introduction

In the current state of scientific knowledge, quantum mechanics is the theory used to describe phenomena that occur at very small scale\footnote{ The way that quantum mechanics has been obtained is very different from the way other theories, relativity for instance, have been obtained. Relativity therory is based on geometric and invariance principles. Quantum mechanics is based on observation (operators are called observables). Gravitational interaction is difficult to describe with the quantum mechanics tools. Einstein, even if he played an important role in the construct of quantum mechanics, was unsatisfied by this theory. His famous "God doesn't play dices" summerizes his point of view. Electromagnetic interaction can be described using quantum dynamics: this is the object of quantum electrodynamics (QED). This will not presented in this book, so the reader should refer to specialized books, for instance ([#References|references]).(atomic or subatomic). The goal of this chapter is to present the mathematical formalism of quantum mechanics. Applications of quantum mechanics will be seen at chapter chapproncorps. Quantum physics relies on a sequence of postulates that we present now. The reader is invited to refer to ([#References|references]) for physical justifications.