I Rotational-Vibrational Energy state equation derivation

1. Apr 5, 2016

EphemeralMurex

I am having a mental block at the moment and for some reason I can't seem to derive these two equations:

From this equation:

Any assistance would be much appreciated!

2. Apr 5, 2016

Staff: Mentor

What have you tried? Do you understand what $\tilde{\nu}_0$ stands for? Otherwise, it's just $T(\nu', J'' \pm 1) - T(\nu'', J'')$.

3. Apr 6, 2016

EphemeralMurex

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?

4. Apr 6, 2016

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:
$$\nu', J' \leftarrow \nu'', J''$$

5. Apr 6, 2016

EphemeralMurex

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