Rotational-Vibrational Energy state equation derivation

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    Derivation Energy State
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Discussion Overview

The discussion revolves around the derivation of rotational-vibrational energy state equations in molecular spectroscopy. Participants explore the meanings of specific variables and seek assistance in the derivation process, focusing on the transition between energy levels.

Discussion Character

  • Homework-related
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant expresses difficulty in deriving specific equations related to rotational-vibrational energy states.
  • Another participant questions the understanding of the variable ##\tilde{\nu}_0## and suggests that it relates to the difference in energy between two states.
  • Confusion arises regarding the notation ##\nu', J''## and ##\nu''##, with one participant incorrectly suggesting they might represent derivatives, while another clarifies that they denote different energy levels in a transition.
  • A participant proposes setting initial values for ##v''## and ##J''## to 0 and ##J'## and ##v'## to 1 as a starting point for the derivation.
  • There is uncertainty about how to manipulate the equation to eliminate certain terms and incorporate specific coefficients such as (2##\beta## - 3##\alpha##) and (2##\beta## - 4##\alpha##).

Areas of Agreement / Disagreement

Participants do not reach a consensus on the derivation process, and multiple viewpoints regarding the interpretation of variables and the steps involved remain unresolved.

Contextual Notes

There are limitations in understanding the definitions and roles of specific variables in the equations, as well as unresolved steps in the derivation process.

EphemeralMurex
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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!
 
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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'')##.
 
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?
 
EphemeralMurex said:
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?
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:
$$
\nu', J' \leftarrow \nu'', J''
$$
 
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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