A Catalogue of Sturm-Liouville Differential Equations

By W. Everitt, B. D. Charles, Franc Sturm. 2005

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An Operator Theoretic Interpretation of the Generalized Titchmarsh-Weyl Coefficient for a Singular Sturm-Liouville Problem (2011, background): “with q0, q1 ∈ R, which is known as the ‘Hydrogen atom differential expression’ (see [14], Section 39), since it appears after separation of variables in twoand three-dimensional Schrödinger equations with Coulomb potential.”
Titchmarsh–Weyl m ‐functions for second‐order Sturm–Liouville problems with two singular endpoints (2008, background): “Instead of relying on a direct application of the Frobenius theory to the Bessel equation as I do in Theorem 2.1 and Corollary 2.4, Everitt and Kalf employ “generalized initial conditions” in their Theorem 6.1 (p. 6) which makes use of wronskian limits as x → 0 of the solutions {φ, θ} being defined,”