Quantization conditions for single-well potentials

When l —1/2 there is on the positive part of the real axis a classically forbidden region in the generalized sense delimited by the origin. It is assumed to be delimited also by a generalized classical turning point t, i.e., a first-order zero of Q2(z). In this region the wave function is 

By means of (4.57) and the connection formula (4.19) one finds that the physically acceptable wave function is given by 

With the base function chosen according to (4.54), it is seen from (4.60) and (4.63) that one obtains the same quantization condition whether l / —1/2 or l = —1/2. It should, however, be emphasized that the motivation for the formulas, on which the quantization condition is based, is quite different in the cases when l / —1/2 and l = -1/2. 

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