Properties of general and partial scattering amplitudes and dispersion relations in quantum mechanics. Part I. Properties of partial scattering amplitudes

The desire to extrapolate the well-developed quantum mechanics scattering theory to acoustic scattering served the stimulus to write the review. Probably this can help in the solution of acoustic problems of scattering, in particular in solution of problems of acoustic radiation pressure calculation. This part of the review states the identity of both problems of scattering. The results of the central potential quantum mechanical scattering are presented. Special attention is given to the description of analytical properties of radial wave functions, Yost functions, partial scattering amplitudes and their features. The equations for the evaluation of partial phase shifts are given. Resonances caused by scattering matrix poles, distinct from the poles corresponding to the bound states are discussed.