Oscillations of a rotating molecule

Our next step will be an attempt to separate rotations and oscillations within the adiabatic approximation. To this end the function fk(R) = 4 ) will be pro- 

No additional approximation is introduced. We say only that the isolated molecule vibrates absolutely independently of whether it is oriented towards the CJapri-com or Taurus Constellations (space is isotropic). The function Xk(R) is yet unknown, therefore dividing by i in (6.20) is meaningless.  

we wDl try to separate the variables 6, 4 from the variable R in eq. (6.18), i.e. to obtain two separate equations for them. First, let us define the quantity 

After inserting the Laplacian (in spherical coordinates, see Appendix H on p. 969) and the product (6.20) into (6.18) we obtain the following series of transformations 

Look The left-hand side only depends on R, and the right-hand side only on 6 and ct . Both sides equal each other independently of the values of the variables. This can only happen if each side is equal to a constant (A), the same for each Therefore, we have 

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