The book presents a new method for solving various diffraction and scattering problems in acoustics, electrodynamics, and quantum mechanics. Each version of the method is based on the representation of the diffracted field in the form of a series in the eigenfunctions of an auxiliary homogeneous problem in which the spectral parameter is usually not the frequency. This allows one to treat problems not only in bounded but also in unbounded domains or in the entire space. For example, for the problem of diffraction on a metallic body, the homogeneous problem of the same form can be used with impedance as the spectral parameter.
The transparency coefficient, the dielectric constant, etc. can also be used as the spectral parameter. The method is especially effective for the analysis of resonance systems, in particular, of open resonators and waveguides. The method permits one to represent the exact solution in unbounded domains in the form of a series (since the spectrum is discrete), without an additional integral with respect to the spectral parameter, and use the variational approach though the corresponding problems are usually nonself-adjoint.