Abstract
We study positivity, localization of binding and essential self-adjointness properties of a class of Schrodinger operators with many anisotropic inverse square singularities, including the case of multiple dipole potentials. 1. Introduction and statement of the main results In this paper we analyze some basic spectral properties of Schrodinger operators associated with potentials possessing multiple anisotropic singularities of degree 2. The interest in such a class of operators arises in nonrelativistic molecular physics, where the interaction between an electric charge and the dipole moment of a molecule con be described by an inverse square potential with an anisotropic coupling strength. More precisely, the Schrodinger operator acting on the wave function of an electron interacting with a polar molecule (supposed to be point-like) can be written as H= ~ 2
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