  Quantum anomalies in the inverse square potential are well known and widely
investigated. Most prominent is the unbounded increase in oscillations of the
particle's state as it approaches the origin when the attractive coupling
parameter is greater than the critical value of 1/4. Due to this unphysical
divergence in oscillations, we are proposing that the interaction gets screened
at short distances making the coupling parameter acquire an effective
(renormalized) value that falls within the weak range 0 to 1/4. This prevents
the oscillations form growing without limit giving a lower bound to the energy
spectrum and forcing the Hamiltonian of the system to be self-adjoint.
Technically, this translates into a regularization scheme whereby the inverse
square potential is replaced near the origin by another that has the same
singularity but with a weak coupling strength. Here, we take the Eckart as the
regularizing potential and obtain the corresponding solutions (discrete bound
states and continuum scattering states).
