Hamiltonian hierarchy and the Hulthén potential.

Abstract

We deal with the Hamiltonian hierarchy problem of the supersymmetry quantum mechanics for the Hulth\'en potential and find that the associated ``supersymmetric partners'' belong to the Eckart class of potentials. The partner potentials, on the one hand, simulate the effect of the centrifugal barrier fairly accurately at least for few lower partial waves and, on the other hand, provide a natural basis for writing expressions for higher partial wave Jost functions. We present specific results for the p and d waves and examine their Coulomb limits.