The zero-mass spinless Salpeter equation with a regularized inverse square potential

We present a detailed study for the classical and the quantum motion of a relativistic massless particle in an inverse square potential. The classical treatment shows that it is possible to find trajectories for which the system has a positive total energy and yet the particle remains bound to the potential center. The quantum approach to the problem is based on the exact solution of the corresponding semirelativistic spinless Salpeter equation for bound states. The connection between the classical and the quantum descriptions is made via the comparison of the associated probability densities for momentum.

► The classical motion of a massless relativistic particle submitted to an attractive inverse square potential is studied.
► The quantum mechanics of the problem is studied via the resolution of the corresponding spinless Salpeter equation for bound states.
► The classical and quantum probability densities for momentum are compared to each other.