Fig. \[Fig\_potentials\](a) (penetration though a barrier is of exponentially small probability) and does not “feel” any barrier in Fig. \[Fig\_potentials\](b) (the particle moves solely in the classically allowed region) while traveling along the axis $\rho=0$, then one would intuitively conclude that the probability of finding the particle in the first quadrant in Fig. \[Fig\_potentials\](a) ought to be smaller than in Fig. \[Fig\_potentials\](b). By the same token, the very same probabilities in Figs. \[Fig\_potentials\](c) and \[Fig\_potentials\](e) should be smaller than in Figs. \[Fig\_potentials\](d) and \[Fig\_potentials\](f), respectively. Further discussions of the phenomenon from the point of view of classical trajectories are presented in Sec. \[Sec4\].

The results presented in Figs. \[Fig\_tunneling\_prob\]–\[Fig\_probability\_tunnel\_time\] are obtained from the numerical solution of the time-dependent Schrödinger equation (\[TimDepSchEq\]) by means of the split-operator method with an absorbing boundary condition. Figures \[Fig\_tunneling\_prob\]–\[Fig\_reflection\_prob\] show the dependence of the probabilities of tunneling, disintegration, and reflection as function of the parameter $\alpha$ that characterizes the asymmetry of the potential barrier. Dynamics of tunneling processes occurring in Figs. \[Fig\_potentials\](a)–(f) are visualized as animations, which are available for viewing in Ref. [@EPAPS_Animations].

Remarkably, while our qualitative conclusion reached regarding Figs. \[Fig\_potentials\](a) and \[Fig\_potentials\](b) is indeed correct (see Fig. \[Fig\_probability\_tunnel\_time\]), the conclusions regarding the 