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I Rotational-Vibrational Energy state equation derivation

  1. Apr 5, 2016 #1
    I am having a mental block at the moment and for some reason I can't seem to derive these two equations:

    IMG_3182.jpg

    From this equation:
    IMG_3181.jpg

    Any assistance would be much appreciated!
     
  2. jcsd
  3. Apr 5, 2016 #2

    DrClaude

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    Staff: Mentor

    What have you tried? Do you understand what ##\tilde{\nu}_0## stands for? Otherwise, it's just ##T(\nu', J'' \pm 1) - T(\nu'', J'')##.
     
  4. Apr 6, 2016 #3
    I guess what confuses me is the ##\nu', J''## and ##\nu''##. I don't know what they mean. Is it the first and second derivative of the original equation?
     
  5. Apr 6, 2016 #4

    DrClaude

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    Staff: Mentor

    No, they are labels to differentiate the different levels involved in the transition, with the double prime indicating the initial state and the prime the final state:
    $$
    \nu', J' \leftarrow \nu'', J''
    $$
     
  6. Apr 6, 2016 #5
    Thank you for that explanation! So to begin deriving the equations, would I set initial values for ##v''## and ##J''## equal 0 and ##J'## and ##v'## to 1 for the ##\tilde\nu##(R)? I also don't understand how to eliminate (##\nu## + ##1/2##) from the equation and bring in the (2##\beta## - 3##\alpha##) and (2##\beta## - 4##\alpha##) values
     
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