  The classical boundaries of the quantum singular oscillator (SO) is addressed
under Weyl-Wigner phase-space and Bohmian mechanics frameworks as to
comparatively evaluate phase-space and configuration space quantum trajectories
as well as to compute distorting quantum fluctuations. For an engendered pure
state \textit{quasi}-gaussian Wigner function that recovers the classical time
evolution (at phase and configuration spaces), Bohmian trajectories are
analytically obtained as to show how the SO energy and anharmonicity parameters
drive the quantum regime through the so-called quantum force, which
quantitatively distorts the recovered classical behavior. Extending the
discussion of classical-quantum limits to a quantum statistical ensemble, the
thermalized Wigner function and the corresponding Wigner currents are computed
as to show how the temperature dependence affects the local quantum
fluctuations. Considering that the level of quantum mixing is quantified by the
quantum purity, the loss of information is quantified in terms of the
temperature effects. Despite having contrasting phase-space flow profiles, two
inequivalent quantum systems, namely the singular and the harmonic oscillators,
besides reproducing stable classical limits, are shown to be statistically
equivalent at thermal equilibrium, a fact that raises the SO non-linear system
to a very particular category of quantum systems.
