Since the past century physics has been using mainly two ways to study and describe the physical world. The first way is through classical physics, a model describing the motion and behaviour of macroscopic objects. The motion of terrestrial bodies, the motion of Earth itself as well as the motion of planets, stars and galaxies, are fully described through classical mechanics and Newton’s laws, laws based on cause and effect. The second way is through quantum physics which refers to the study of the microcosm, of molecules, atoms and fundamental particles, things which Newtonian physics is insufficient to describe as the nature of the microcosm is probabilistic and not deterministic. The correspondence principle predicts that the resulting behavior of systems described by the theory of quantum mechanics reproduces the results of classical physics in a specific limit and that the latter can describe the phenomena of these systems. This happens in the limit of large quantum numbers, meaning the study of macroscopic bodies. Under that scope, classical mechanics is essentially considered as a limit state of quantum mechanics, a, by definition, more fundamental theory. Erwin Schrödinger, in 1926, first grappled with the proof of the principle of correspondence. He formulated that in coherent states of the quantum harmonic oscillator there are minimum uncertainty Gaussian wave packets which satisfy the Schrödinger equation. In a coherent state the expected values of the Heisenberg picture are the exact same with the equations of motion of classical mechanics and exhibit little dispersion in high energies. Schrödinger tried to extend his theory unto more complex systems but this proved infeasible due to computational problems. It was only thirty years ago when the interest in the classical limit was rekindled and it was even later, in 2005, when Roy J. Clauber would win the Nobel prize for his contribution in the quantum theory of optical coherence.
Coherent states represent the kind of quantum states of the quantum harmonic oscillator that exist as close as possible to the classical limit. It is as close as we have ever gotten to connecting the completely deterministic macrocosm and the predictability of classical physics with the chaotic probabilistic microcosm of quantum mechanics.