About properties of wave functions and tsub(e)-matrix in the case of potentials with hard core

Some analytical properties of wave functions for a sufficiently broad class of potentials containing a hard core have been investigated. For such potentials conditions of completeness of the wave functions outside the hard core has been proved. Using properties of regular and irregular solutions one finds the contribution from the hard core to the expression for tsub(e) scattering matrix. On this basis tsub(e) matrix is constructed and its analytical structure is being investigated. From the analytical structure of the tsub(e) matrix it follows that the bound states appears in the system of two particles interacting via the hard core only when the potential presents outside the hard core. A comparative analysis of various methods for taking into account for the hard core is presented