Abstract
We present a complete analytical solution to the quantum problem of a particle in the Yukawa potential, using supersymmetry and a systematic expansion of the corresponding super-potentials. Results for the critical screening of the ground state improve in several figures existing results based on both numerical solutions and approximation methods. Our calculation to order (a0/D)2 for the squared ground state wavefunction at the origin, which enter in darkonium transitions, yields a correction of π4/216 to results based on variational techniques.
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