Best Of Both Worlds

Any velocity along $x$, a radial line joining the particle and the center of the $\psi$ cloud will result in oscillations.

So all roots, positive and negative, to the factor,

$e^u(e^{2u}-1)^{1/2}$

are admissible.  And we have both circular motion and oscillation where the two velocities, circular motion velocity and instantaneous oscillation velocity, are perpendicular at all times.

Good night.