In classical mechanics, an asymmetric rotating object will generally precess. Expressed in the body-fixed normal system of the object, we have [itex]I_i \dot{\omega_i}=(\vec{L}\times \vec{\omega})_i[/itex] where [itex]L_i=I_i\omega_i[/itex].(adsbygoogle = window.adsbygoogle || []).push({});

Choosing a simple example where [itex]I_1=I_2[/itex], we obtain [itex]\dot{\omega_3}=0[/itex] and, for [itex]\Omega=\frac{I_1-I_3}{I_1}\omega_3[/itex],

[itex]\dot{\omega_1}=\Omega \omega_2[/itex]

[itex]\dot{\omega_2}=-\Omega \omega_1[/itex]

describing the precession. Thus, [itex]\vec{\omega}(t)=(A\cos(\Omega t) , A\sin(\Omega t), \omega_3)[/itex].

My question is; can this motion be described quantum mechanically?

My first guess was to write the Hamiltionian as [itex]\hat{H}=\frac12 \hat{\vec{\omega}}I\hat{\vec{\omega}}[/itex] with [itex]I[/itex] being the inertia tensor. The difficulty is then to describe [itex]\hat{\vec{\omega}}[/itex] in terms of [itex]\hat{x},\hat{p_x}[/itex] etc.

Am I going about this the wrong way?

Is there any treatment of this problem available? I tried searching, but all the treatments of precession I found were related to magnetic moment precession.

Any help is greatly appreciated.

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# Torque-free precession

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