Generalized Bertlmann–Martin inequalities and power-law potentials

Abstract

In the three-dimensional Schr€odinger equation, the generalized Bertlmann–Martin inequalities connect the moments of the ground state density to the energy differences between the lowest level of each angular momentum ‘ and the ground state. They are discussed in the case of the power-law potentials, as well as the ln r potential. Use is made of the derived moments to reconstruct the form factor F ðqÞ, i.e., the Fourier transform of the ground state density. Pad e approximants are used to describe the high q behavior of the form factor when only a limited number of low order moments are known. The estimate of the ground state density at the origin is also discussed