Minimum rotation of long carbon nanotube

[Ray Gardener]

I was wondering, given the behavior of quantized rigid rotors, what
would happen if a long and perfectly straight carbon nanotube were to be
slowly spun around its midpoint like a propeller. Would the quantized
rotation angle at the center be magnified at the ends of the tube to be
macroscopically measurable? Would the tube rotate in discrete steps?

Ray

[Igor Khavkine]

Ray Gardener wrote:
> I was wondering, given the behavior of quantized rigid rotors, what
> would happen if a long and perfectly straight carbon nanotube were to be
> slowly spun around its midpoint like a propeller. Would the quantized
> rotation angle at the center be magnified at the ends of the tube to be
> macroscopically measurable? Would the tube rotate in discrete steps?

You seem to be under the impression that the rotation angle for a
quantum rotor is quantized. That is not so, it is its conjugate
variable, angular momentum, that is quantized. There is still a
continuum of possible angular orientations.

If the rod is rotating slowly enough (really small angular momentum
implies quantum mechanical effects), then you'll be able to see jumps
in its angular momentum as it is sped up. But if you do get it into a
state where you can observe its rotation, it will be continuous and
pretty much classical. Low angular momentum/energy states, where
quantum effects are visible, are stationary. That is, instead of moving
around, the rod's probability amplitude will be spread out over all
possible angular directions. Think about the ground state of the
electron in the hydrogen atom.

Hope this helps.

Igor