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Deriving hamiltonian operator for rotational kinetic energy.

  1. Jan 16, 2016 #1

    georg gill

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    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

    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

    3. The attempt at a solution

    upload_2016-1-16_9-0-25.png
     
  2. jcsd
  3. Jan 16, 2016 #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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