Bound states of a short-range potential with inverse cube singularity
arXiv:1805.07153 · doi:10.1142/S0217732319502237
Abstract
We use the Tridiagonal Representation Approach (TRA) to obtain exact bound states solution (energy spectrum and wavefunction) of the Schrödinger equation for a three-parameter short-range potential with 1/r, 1/r^2 and 1/r^3 singularities at the origin. The solution is a finite series of square integrable functions with weighted coefficients that satisfy a three-term recursion relation. The solution of the recursion is the discrete version of a non-conventional orthogonal polynomial. We are currently preparing to use the results of this work to study the binding of an electron to a molecule with an effective electric quadrupole moment, which has the same 1/r^3 singularity.
17 Pages, 1 Table, 5 Figures
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