The determination of the internal structure of relativistic astrophysical objects in the wave approximation

General relativity theory is used to examine spherically symmetric inverse problems for the scattering of quantum particles by a static gravitational field. Methods are developed for reconstructing the metric tensor from scattering data in the case of a fixed energy or zero angular momentum for the Klein-Fock-Gordon equation in the Schwarzschild metric. The main elements of the algorithms developed are two definite nonlinear ordinary differential equations of the third and fourth order based on the scattering data. The motion of a scalar particle in a strong gravitational field is shown to be analogous to the motion in a field with a potential dependent on the angular momentum or energy in nonrelativistic quantum mechanics.