The problem of N quantum-mechanical equal particles interacting pairwise by inverse-cube forces (``centrifugal potential'') in addition to linear forces (``harmonical potential'') is considered in a onedimensional space. An explicit expression for the ground-state energy and for the corresponding wavefunction is exhibited. A class of excited states is similarly displayed.

Journal of Mathematical PhysicsDec 1, 1969550 citations

Inverse-square potential and the quantum vortex

Hua Wu, Donald W. L. Sprung

The vortex structure of the steady-state probability flow for a general one-particle system in quantum mechanics is introduced and its relationship to the inverse-square potential is discussed. The relationship is made clear by classifying the corresponding solutions of the related classical inverse-square-potential problem.

Physical Review AJun 1, 199438 citations