Exactly solvable models of delta(')-sphere interactions in nonrelativisticquantum mechanics

We introduce and perform a systematic study of a new exactly solvable model of sphere interactions in quantum mechanics : the delta(') interaction, fo rmally given by -Delta+alpha delta(')(\ x \-R), <x is an element of R-3, R > 0, alpha is an element of R. We also consider the cases of a delta(') plu s a Coulomb interaction and finitely many delta(')-sphere interactions with support on concentric spheres. For all these models, we provide basic prop erties and discuss the stationary scattering theory. We also briefly discus s the delta(')-sphere interaction of the second type. (C) 1999 American Ins titute of Physics. [S0022-2488(99)02508-6].