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.
