Closed-form solutions of the Schroedinger equation for a class of smoothed Coulomb potentials
classification
⚛️ physics.atom-ph
math-phmath.MP
keywords
closed-formequationschroedingersolutionsangularapproximateclasscoulomb
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An infinite family of closed-form solutions is exhibited for the Schroedinger equation for the potential $V(r) = -Z/\sqrt{|r|^{2} + a^{2}}$. Evidence is presented for an approximate dynamical symmetry for large values of the angular momentum $l$.
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