The Maslov index for composite power-law potentials: The case of the first Exton potential

Using the exact solution of the one-dimensional Schrödinger equation, we demonstrate that the Maslov index involved in the Bohr-Sommerfeld semiclassical quantization rule for the first Exton potential depends on the intensity parameters of the potential. As a function of the intensity of the potential term proportional to x−3/2, it varies within a rather wide range, from −1 to 0, adopting −1/6 when this term and its conjugate term ∼x−1, are absent, which is the case when the Exton potential reduces to the inverse-square-root potential.