  It is known that for a non-relativistic quantum particle traveling freely on
the $x$-axis, the positional probability can flow in the opposite direction to
the particle's velocity. The maximum possible amount of such backflow that can
occur over any time interval has been determined previously as the largest
positive eigenvalue of a certain hermitian observable, with the value
$0.0384517\dots$, or about $4\%$ of the total probability on the line. The
eigenvalue problem is now considered numerically in the more general case of
states with momentum restricted to the range $p_0<p<\infty$, for any given
value $p_0$. It is found that the maximum possible backflow decreases
monotonically, but never reaches $0$, as $p_0$ increases through positive
values; and it increases monotonically, but never reaches $1$, as $p_0$
decreases through negative values. Both of these effects are non-classical. The
results allow a simple interpretation of the classical limit, as an effective
value of Planck's constant goes to zero and probability backflow becomes
impossible.
