= Solution
For the separated <stationary state>, restore its time factor $e^{-iEt/\hbar}$. Away from radial nodes, the <quantum phase> is $S=k\phi-Et/\hbar$, up to a constant $0$ or $\pi$ where the real radial function has fixed sign. The <guidance equation> in <plane polar coordinates> therefore gives the <Bohmian circulation of an angular-momentum eigenstate>
$$
\boxed{v_r=0,\qquad v_\phi=\frac{\hbar k}{mr},\qquad |\mathbf v|=\frac{\hbar|k|}{mr}}.
$$
The direction is $\widehat{\boldsymbol\phi}$ for $k>0$ and $-\widehat{\boldsymbol\phi}$ for $k<0$; the velocity is zero for $k=0$. Each admissible trajectory is a circle:
$$
r(t)=r_0,\qquad \phi(t)=\phi_0+\frac{\hbar k}{m r_0^2}t.
$$
The <orbital angular momentum> along the trajectory is $mr_0v_\phi=\hbar k$. The origin or any zero-amplitude circle is excluded from this local formula. For the real degenerate superposition constructed above, the spatial <quantum phase> is constant on each nodal sector, so its <Bohmian mechanics> velocity is instead zero. Thus the circular motion is a conclusion about the separated angular-momentum <eigenstate>, not an arbitrary energy <eigenstate>.
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