Quantization of the highest levels in a molecular potential

Abstract

The position of the highest level in a molecular potential is not well describedby the usual JWKB quantization formula. This is due to an effect which is themirror image for bound states of the quantum threshold behaviour for the continuumstates. This new effect is described in the present letter and some consequencesare briefly discussed. In particular, we discuss the probability distribution ofthe binding energy of the highest vibrational level and show that its shape isstrongly modified.