In this paper we discuss the general form of a wave equation which in particular may be a SCHRÖDINGER, DIRAC, KLEIN-GORDON equation. Under certain assumptions we obtain the necessary and sufficient condition for analytic continuability of its solutions considered as meromorphic functions. Next, we obtain some general formulae in the scattering theory for a potential of arbitrary symmetry. The values of scattering matrix elements are determined by the wave functions for the discrete energy spectrum and by their analytic continuations. Our theoretical results are applied to the deuteron disintegration problem and the phase shift calculation for a modified YUKAWA potential.