Abstract
We introduce and perform a systematic study of a new exactly solvable model of sphere interactions in quantum mechanics : the δ′ interaction, formally given by −Δ+αδ′(|x|−R), x∈R3, R>0, α∈R. We also consider the cases of a δ′ plus a Coulomb interaction and finitely many δ′-sphere interactions with support on concentric spheres. For all these models, we provide basic properties and discuss the stationary scattering theory. We also briefly discuss the δ′-sphere interaction of the second type.
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