Precision methods for solving the Schrödinger equation with singular potentials in momentum space
A high precise calculation of various energy corrections of the hydrogen-like systems is a relevant problem since the experimental measurements of such values are performed with high accuracy. We use new special quadrature formulas for singular and hypersingular integrals to numerically solve the Schrödinger equation in momentum space with the linear confinement potential, Coulomb and Cornell potentials. It is shown that the energy spectrum of a quantum system can be calculated with an accuracy far exceeding other calculation methods. These methods are easily generalized to the relativistic equations, where the potentials are generally derived in momentum space. Consequently, the developed procedure to obtain the energy spectra can be used to study and calculate various effects in the two-body quantum systems, such as hydrogen-like atoms, hadronic atoms and bound quark systems.