  In this paper, I present a mapping between representation of some quantum
phenomena in one dimension and behavior of a classical time-dependent harmonic
oscillator. For the first time, it is demonstrated that quantum tunneling can
be described in terms of classical physics without invoking violations of the
energy conservation law at any time instance. A formula is presented that
generates a wide class of potential barrier shapes with the desirable
reflection (transmission) coefficient and transmission phase shift along with
the corresponding exact solutions of the time-independent Schr\"odinger's
equation. These results, with support from numerical simulations, strongly
suggest that two uncoupled classical harmonic oscillators, which initially have
a 90\degree relative phase shift and then are simultaneously disturbed by the
same parametric perturbation of a finite duration, manifest behavior which can
be mapped to that of a single quantum particle, with classical 'range
relations' analogous to the uncertainty relations of quantum physics.
