A More Accurate Treatment. The Morse Function

A More Accurate Treatment. The Morse Function.— The simple treatment which we have just given fails to agree with experiment in that it yields equally spaced levels, whereas the observed vibrational levels show a convergence for increasing values of v. In order to obtain this feature a potential function U(r) is required which is closer to the true U(r) described in 

1 This is seen by allowing k to become infinite, causing the third term to vanish (because - — ). A rigid molecule would have no vibrational energy, so the first term would become an additive constant. The rigid rotator is often discussed as a separate problem, with the wave equation 

The rigid rotator is of course an idealization which does not occur in nature. 

Another idealized problem is the rigid rotator in a plane, for which the wave equation is 

Section 356, especially with regard to its behavior for large values of r. 

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