Abstract
Comparison equation technique, with the Coulomb potential plus the centrifugal barrier as comparison potential, is applied to the Schrödinger equation when there are turning points close to a pole of the potential. By asymptotic expansion, with respect to a “small” parameter, of the resulting formal solution one obtains the arbitrary-order phase-integral approximation generated from an unspecified base function. The phase and the amplitude of the phase-integral solution thus obtained remain accurate also when the turning points lie close to the pole. For a solution that is regular at the pole of the potential the results yield new phase-integral formulas in the classically allowed region. These formulas contain as special limiting cases previously known formulas, valid when the turning points recede from the pole. The normalization of the wave function is also considered.
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Fröman, N., Fröman, P.O., Linnaeus, S. (1996). Phase-Integral Formulas for the Regular Wave Function When There Are Turning Points Close to a Pole of the Potential. In: Phase-Integral Method. Springer Tracts in Natural Philosophy, vol 40. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2342-9_6
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DOI: https://doi.org/10.1007/978-1-4612-2342-9_6
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