  It is first shown that when the Schr\"{o}dinger equation for a wave function
is written in the polar form, complete information about the system's {\em
quantum-ness} is separated out in a single term $Q$, the so called `quantum
potential'. An operator method for classical mechanics described by a
`classical Schr\"{o}dinger equation' is then presented, and its similarities
and differences with quantum mechanics are pointed out. It is shown how this
operator method goes beyond standard classical mechanics in predicting coherent
superpositions of classical states but no interference patterns, challenging
deeply held notions of classical-ness, quantum-ness and macro realism. It is
also shown that measurement of a quantum system with a classical measuring
apparatus described by the operator method does not have the measurement
problem that is unavoidable when the measuring apparatus is quantum mechanical.
The type of decoherence that occurs in such a measurement is contrasted with
the conventional decoherence mechanism. The method also provides a more
convenient basis to delve deeper into the area of quantum-classical
correspondence and information processing than exists at present.
