Some Energy Inequalities for Two-Body Problems and Helium Dimer

Abstract

It is shown that the energy of two particles in 2D (2 dimensions) is always less or equal than energy in 1D, and the energy in 3D can be less or greater than in 2D. The application to the important case of helium 4 direr shows that this molecule may have only in 2D at least one bound excited state PACS numbers: 36.90.+f