= Classical limit
{wiki}
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 $d\langle P\rangle/dt=-\langle V'(X)\rangle$. Approximating the force average by $-V'(\langle X\rangle)$ 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.
Back to article page
