  There are no phase-space trajectories for anharmonic quantum systems, but
Wigner's phase-space representation of quantum mechanics features Wigner
current~$\bf J$. This current reveals fine details of quantum dynamics -- finer
than is ordinarily thought accessible according to quantum folklore invoking
Heisenberg's uncertainty principle. Here, we focus on the simplest, most
intuitive, and analytically accessible aspects of~$\bf J$. We investigate
features of~$\bf J$ for bound states of time-reversible, weakly-anharmonic
one-dimensional quantum-mechanical systems which are weakly-excited. We
establish that weakly-anharmonic potentials can be grouped into three distinct
classes: hard, soft, and odd potentials. We stress connections between each
other and the harmonic case. We show that their Wigner current fieldline
patterns can be characterised by~$\bf J$'s discrete stagnation points, how
these arise and how a quantum system's dynamics is constrained by the
stagnation points' topological charge conservation. We additionally show that
quantum dynamics in phase space, in the case of vanishing Planck constant
$\hbar$ or vanishing anharmonicity, does not pointwise converge to classical
dynamics.
