“Fall toward the centre” in quasipotential theory

A study is made of the quasipotential equation for the wave function in the momentum space in the case of the singular attractive potential $U(r)=-\lambda r^{-2}$. It is shown that in the nonrelativistic limit the discrete spectrum does not depend on the arbitrary constant and is characterized by the presence of a finite ground state, i.e., in it there is no “fall toward the center” problem. These results are a consequence of the self-adjointness of the quasipotential operator in the momentum space (deficiency index $n=0$), in contrast to the Lippmann-Schwinger operator (deficiency index $n=1$).