The Formulation of Wave Mechanics

Abstract

We introduce the basic physical ideas of Quantum Mechanics following the line of thought of Schrodinger Wave Mechanics. Exploiting the analogy between Optics and Mechanics, we arrive at the formulation of the Schrodinger equation. Moreover, Born’s statistical interpretation of \(|\psi |^2\) is explained with some details. We also introduce the representation of the observables as linear operators in a Hilbert space and we discuss Heisenberg uncertainty relations as a consequence of the non commutativity of position and momentum observables. Finally, a first introduction to the idea of classical limit of Quantum Mechanics is given. In this chapter, the emphasis is on the physical ideas rather than on mathematical rigor. Nevertheless, it is underlined that a more precise and mathematically consistent formulation of the theory requires notions of the theory of linear operators in Hilbert spaces that will be discussed in Chap. 4.