# Deriving hamiltonian operator for rotational kinetic energy.

1. Jan 16, 2016

### georg gill

1. The problem statement, all variables and given/known data

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.
2. Relevant equations

By using algebra we obtain:

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

3. The attempt at a solution

2. Jan 16, 2016

### vela

Staff Emeritus
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.