Abstract
The authors discuss exactly solvable Schrodinger Hamiltonians corresponding to a surface delta interaction supported by a sphere and various generalisations thereof. First they treat the pure delta sphere model; self-adjointness of the Hamiltonian, spectral properties, stationary scattering theory, approximation by scaled short-range Hamiltonians. Next they 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 delta ' sphere interaction, first taken alone, then superimposed on a point interaction or a Coulomb potential.