2 N Parameters models of finitely many nonrelativistic of δ' sphere and δ' sphere plus coulomb interactions in quantum mechanics

Abstract

We make a systematic study of new exactly solvable models of 2 N parameters models of finitely many nonrelativistic δ'-sphere and δ'-sphere plus Coulomb interactions. They constitute a generalization of 2N parameters nonrelativistic δ'-sphere and δ'-sphere plus Coulomb interactions. We provide the mathematical definitions of hamiltonians and obtain new results for both model, in particular the resolvents equations, spectral properties and some scattering quantities theory. When we have an appropriate choice of the parameters linked to the above-mentioned model, we show that the unification of the δ'-sphere interactions of the first and second type leads to an increase in scattering amplitude and a decrease of scattering length.