  In some parameter and solution regimes, a minimally coupled nonrelativistic
quantum particle in 1d is isomorphic to a much heavier, vibrating, very thin
Euler-Bernoulli rod in 3d, with ratio of bending modulus to linear density
$(\hbar/2m)^2$. For $m=m_e$, this quantity is comparable to that of a
microtubule. Axial forces and torques applied to the rod play the role of
scalar and vector potentials, respectively, and rod inextensibility plays the
role of normalization. We show how an uncertainty principle $\Delta x\Delta
p_x\gtrsim\hbar$ governs transverse deformations propagating down the
inextensible, force and torque-free rod, and how orbital angular momentum
quantized in units of $\hbar$ or $\hbar/2$ (depending on calculation method)
emerges when the force and torque-free inextensible rod is formed into a ring.
For torqued rings with large wavenumbers, a ``twist quantum'' appears that is
somewhat analogous to the magnetic flux quantum. These and other results are
obtained from a purely classical treatment of the rod, i.e., without quantizing
any classical fields.
