Relationships between potential functions and the vibration-rotation levels

Relationships between potential functions and the vibration-rotation levels 

Earlier in this chapter we discussed the ab initio calculation of diatomic molecule potential functions these may be expressed as the sum of the potential for a rotationless molecule, and a rotational energy term, 

Given the potential energy curve Vj(R) it is possible, through an iterative procedure which we describe shortly, to locate the vibrational levels using the semiclassical quantisation condition 

S (R) and S (R) are the first- and second-derivatives of S(R) with respect to R. The one-dimensional Schrodinger equation, 

We now return to equations (6.367) and (6.368), and extract the terms which are linear in h, obtaining the results 

The JWKB semiclassical method The Schrodinger equation can be written in the form 

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