On the two-dimensional Schrödinger operator with an attractive potential of the Bessel–Macdonald type

We analyze the Schrödinger operator in two-dimensions with an attractive potential given by a Bessel–Macdonald function. This is derived non-relativistic approximation of planar quantum electrodynamics (QED3) models as framework for evaluation two-quasiparticle scattering potentials. The analysis motivated keeping mind fact that parity-preserving QED3 can provide possible explanation behavior superconductors. Initially, we study self-adjointness and spectral properties modeling these models. Then, using Setô-type estimates, estimate number two-particle bound states which depends directly on value effective coupling constant, C, any angular momentum. In fact, this result connection condition guarantees shows there always be large particular, show existence isolated state if constant C?(0,2) case zero To best our knowledge, has not yet been addressed literature. Additionally, obtain explicit energy gap might applied to high-Tc s-wave Cooper-type superconductors well electron–polaron–electron–polaron (bipolarons) mass-gap graphene systems.