Abstract
We solve the phase shifts of Lennard-Jones potential at low energy by the modified WKB approximation in order to demonstrate the validity of the modified WKB approximation. We choose to solve exactly a model three-turning-point problem. The differences between the potentials of the actual and the model problem are taken care of by WKB type perturbations. We report here the detailed calculations to the order of ℏ2. Although the model potential is somewhat different from the actual potential (except that they have an equal number of turning points), the higher order terms do contribute to such an extent that the agreement of the phase shifts with the numerical values is satisfactory even near the maximum of the potential where the conventional WKB method is known to fail.
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