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Bryenton, Nasser Saad, Richard L Hall","submitted_at":"2018-10-15T17:42:01Z","abstract_excerpt":"An analysis of the generalized confluent Heun equation $(\\alpha_2r^2+\\alpha_1r)\\,y''+(\\beta_2r^2+\\beta_1r+\\beta_0)\\,y'-(\\varepsilon_1r+\\varepsilon_0)\\,y=0$ in $d$-dimensional space, where $\\{\\alpha_i, \\beta_i, \\varepsilon_i\\}$ are real parameters, is presented. With the aid of these general results, the quasi exact solvability of the Schr\\\"odinger eigenproblem generated by the softcore Coulomb potential $V(r)=-e^2Z/(r+b),\\, b>0$, is explicitly resolved. Necessary and sufficient conditions for polynomial solvability are given. 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