Deriving hamiltonian operator for rotational kinetic energy.

[georg gill]

Homework Statement

I am trying to get the hamiltonain operator equality for a rigid rotor. But I don't get it. Please see the red text in the bottom for my direct problem. The rest is just the derivation I used from classical mechanics.

Homework Equations

By using algebra we obtain:

By using this definition K of rotational kinetic energy one writes:

The Attempt at a Solution

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[vela]

You can show that
$$K = \frac 12 \mu (r\omega)^2 = \frac 12 (\mu r^2)\omega^2 = \frac 12 I \omega^2 = \frac{L^2}{2I},$$ where $L$ is the angular momentum of the system.