The classical limit is a concept in physics that refers to the behavior of quantum systems as they transition to classical systems, typically as certain parameters approach appropriate limits. It describes the conditions under which quantum mechanical systems can be approximated by classical mechanics. Here are a few key points about the classical limit: 1. **Planck's Constant**: One of the most important factors in the classical limit is Planck's constant (h).
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The classical limit is a regime in which specified observables of a quantum system are approximated by classical mechanics or classical field equations. It is a statement about scales, states and measurements, rather than simply about an object being large.
For a narrow wave packet in a smoothly varying potential energy, Ehrenfest theorem gives . Approximating the force average by yields a classical trajectory while the packet remains sufficiently narrow. Strong spreading or quantum tunnelling can invalidate it. For highly occupied bosonic modes, occupation-number discreteness can likewise become relatively small, yet quantum interference can remain observable when relative quantum phases are preserved. A useful classical limit must therefore specify which predictions the approximation reproduces.
The idea tha taking the limit of the non-classical theories for certain parameters (relativity and quantum mechanics) should lead to the classical theory.
It appears that classical limit is only very strict for relativity. For quantum mechanics it is much more hand-wavy thing. See also: Subtle is the Lord by Abraham Pais (1982) page 55.