Exactly solvable models of sphere interactions in quantum mechanics

We discuss exactly solvable Schrodinger Hamiltonians corresponding to a surface delta interaction supported by a sphere and various generalisations thereof.First we treat the pure S sphere model: self-adjointness of the Hamiltonian, spectral properties, stationary scattering theory, approximation by scaled short-range Hamiltonians.Next we extend the model by adding a point interaction at the centre of the sphere or, alternatively.a Coulomb interaction.Finally the whole analysis is extended to the case of a 8' sphere interaction, first taken alone, then superimposed on a point interaction or a Coulomb potential.