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Deriving hamiltonian operator for rotational kinetic energy.

  • Thread starter georg gill
  • Start date
  • #1
georg gill
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1

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



upload_2016-1-16_8-57-32.png


By using algebra we obtain:

upload_2016-1-16_8-58-19.png


By using this defintion K of rotational kinetic energy one writes:
upload_2016-1-16_8-59-51.png


The Attempt at a Solution



upload_2016-1-16_9-0-25.png
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Answers and Replies

  • #2
vela
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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.
 

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