The classical boundaries of the quantum singular oscillator (SO) are 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 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.

在Weyl–Wigner相空间和Bohmian力学框架下，解决了量子奇异振荡器（SO）的经典边界问题，以便比较地评估相空间和构型空间的量子轨迹以及计算扭曲的量子涨落。对于产生的纯态准-高斯Wigner函数可恢复经典的时间演化（在相空间和配置空间），可通过分析获得鲍姆轨道，以表明SO能量和非谐参数如何通过所谓的量子力驱动量子态，从而定量地恢复了恢复态经典行为。将经典量子极限的讨论扩展到量子统计集合，计算热化的维格纳函数和相应的维格纳电流，以表明温度依赖性如何影响局部量子涨落。考虑到量子混合的程度是由量子纯度来量化的，信息的损失是根据温度效应来量化的。尽管相空间流轮廓不同，但两个不等价的量子系统