The relationship between classical mechanics and quantum mechanics has been a subject of longstanding discussion ever since the advent of quantum mechanics. A related question has been the probabilistic nature of the quantum mechanical description, in particular, whether the probabilistic nature of QM description is intrinsic or is attirutable to some unspecifiable "hidden parameters" belonging to the system.
The wave nature of matter that is characteristic of quantum behaviour is known to come into play for miscroscopic dimensions and small effective masses. The "classical limit" is generally taken to be . In this limit, the quantum description should pass over into the classical description. But the precise manner of transition is far from clear. In particular, it may be noted, in this connection, that classical mechanics is an initial value problem being governed by a second order ordinary differential equation in this for the position coordinates. They advance the initial values in time pertaining to positions and momenta. An important tenet of classical mechanics is that the whole continuum of initial values are allowed values. Consequently, all the possible states of motion constrained only by the equation of motion are allowed. In particular, all the continuum of energy states are allowed.