The two dimensional motion of a particle in an inverse square potential: Classical and quantum aspects

The classical 2D dynamics of a particle moving under an inverse square potential, -k/r(2), is analysed. We show that such problem is an example of a geometric system since its negative energy orbits are equivalent to free motion on a certain hypersurface. We then solve in momentum space, the corresponding unrenormalized quantum problem showing that there is no discrete energy spectrum and, particularly, no ground state. (C) 2013 AIP Publishing LLC.