Numerical Solution of Equations Containing an Unknown under the Integral Sign. Application to the Solution of Physical Problems

Abstract

The solution of equations containing an unknown under the integral sign with the help of computer mathematics systems is considered. A rational solution of the equation in the problem of determining impurities by means of laser sensing of the atmosphere is proposed. It is shown how to numerically determine the energy spectrum of quantum systems in the quasi-classical approximation using the Bohr-Sommerfeld quantization condition. Solutions of equations containing Bessel functions in integral representation in the following problems are given: about diffraction of light on opaque disk, about diffusion of magnetic field in hollow cylinder, about determination of critical size of nuclear reactor. The spectrum of Rydberg states of hydrogen atom in electric field is found. A method for determining the thermodynamic properties of relativistic fermi-gas is proposed.