Page "Quantum mechanics" Paragraph 35

The rules of quantum mechanics are fundamental.

They assert that the state space of a system is a Hilbert space, and that observables of that system are Hermitian operators acting on that space — although they do not tell us which Hilbert space or which operators.

These can be chosen appropriately in order to obtain a quantitative description of a quantum system.

An important guide for making these choices is the correspondence principle, which states that the predictions of quantum mechanics reduce to those of classical mechanics when a system moves to higher energies or — equivalently — larger quantum numbers, i. e. whereas a single particle exhibits a degree of randomness, in systems incorporating millions of particles averaging takes over and, at the high energy limit, the statistical probability of random behaviour approaches zero.

In other words, classical mechanics is simply a quantum mechanics of large systems.

This " high energy " limit is known as the classical or correspondence limit.

One can even start from an established classical model of a particular system, then attempt to guess the underlying quantum model that would give rise to the classical model in the correspondence limit.