Application of the Secondhyphen;Order WBK Approximation to Radial Problems

摘要

When the WBK approximation is applied to radial problems, difficulties are encountered at the origin. Previous work has led to the conclusion that the difficulties are removed by substitution of (J+frac12;)2forJ(J+1) in the effective potential. The use of (J+frac12;)2is here shown to be justified for the firsthyphen;order WBK approximation only. The secondhyphen;order WBK wavefunction is found to approximate the exact one asrrarr;0, if one substitutesKforJ(J+1), whereKobeys the equationK+1/(64K)=J(J+1). Moreover, the secondhyphen;order WBK energy levels can be made to coincide with the exact levels for the hydrogen atom and for the radial harmonic oscillator if the same substitution is made. Implications with regard to the rotating vibrator problem are discussed.