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The Schrödinger–Coulomb problem in ℝ N , N ≥ 2, is considered in the momentum representation. The adjoint Sturmian eigenvalue problem is discussed first. The resulting radial integral equation is solved with the aid of a symmetric Poisson‐type series expansion of the Legendre function of the second kind into products of the Gegenbauer polynomials, established in the 1950's by Ossicini. A relationship between solutions to the Sturmian problem and to an energy eigenvalue problem is then exploited to find the Coulomb bound‐state energy levels in ℝ N , together with explicit representations of the associated momentum‐space wave functions.

Alternative approach to the solution of the momentum‐space Schrödinger equation for bound states of the N‐dimensional Coulomb problem