Singular anharmonicities and the analytic continued fractions. II. The potentials V(r)=a r2+b r−4+c r−6

Publisher Website
Google Scholar
Abstract
The c=0 results of Paper I [J. Math. Phys. 3 0, 23 (1989)] are extended. In spite of the presence of an additional coupling constant, the Laurent series solutions of the Schrödinger equation that are obtained remain similar to Mathieu functions. Indeed, the recurrences for coefficients preserve their three‐term character, their analytic continued fraction solutions still converge, etc. The formulas become even slightly simpler for c≠0 due to a certain symmetry of the equations to be solved. An acceleration of convergence is better understood and a few numerical illustrations of efficiency are also delivered.