Authors: Spiros Konstantogiannis
Using a length scale, we construct an n-independent, one-dimensional shifted Coulomb potential, which, with the addition of a delta potential with n-dependent coupling, forms a quasi-exactly solvable model. Making a polynomial ansatz for the closed-form eigenfunctions, we obtain a three-term recursion relation, from which the known energies are derived and the polynomial coefficients are factorized. The coupling is then written in terms of a continued fraction, which, as n tends to infinity, reveals a triangular symmetry and converges. Finally, the location of the closed-form eigenfunctions is determined and the first ones are examined.
Comments: 49 Pages.
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