The spectrum of a Schrodinger operator with the zero-radius potential in a
nanostructure of a constant total curvature is considered. Positions of the
coupled states in a well of zero radius and the corresponding binding ener
gy are determined. Their dependence on the scattering length and curvature
is studied. The condition of the formation of the coupled state is determin
ed. (C) 2000 MAIK "Nauka/Interperiodica".