The Principle of Critical Action and the Harmonic Oscillator – Ariadne’s Thread in Classical Mechanics

The aim of this and the following chapter is to explain the basic physical and mathematical ideas of classical mechanics and quantum mechanics by considering the so-called harmonic oscillator. In all fields of physics, one encounters oscillating systems. Let us mention the following examples:

• • electromagnetic waves and light (photons);

• • laser beams (coherent states);

• • oscillating molecules in a gas or a liquid;

• • sound waves (phonons);

• • oscillations of a crystal lattice (phonons);

• • oscillations of a string (e.g., a violin string);

• • waves in a plasma (plasmons);

• • matter waves of elementary particles (e.g., electrons);

• • gravitational waves (gravitons).