Axioms of Quantum Mechanics and the Hilbert Space

In this and the following sections, we summarize the main assumptions underlying quantum mechanics and clarify its mathematical structure. We will discuss the concept of the Hilbert space of quantum states, orthogonality and superposition of wave functions, and the representation of physical variables like the momentum or the energy as operators. This slightly more abstract point of view will help us enormously to extend the theory to many other physical systems, and to find a clear language for describing them.

In the preceding section we have already introduced all the required components we need to construct the main theory.