Precision methods for solving the Schrödinger equation with singular potentials in momentum space

  • Viktor V. Andreev Francisk Skaryna Gomel State University, 104 Saveckaja Street, Gomel 246019, Belarus

Abstract

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 relati-vistic 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.

Author Biography

Viktor V. Andreev, Francisk Skaryna Gomel State University, 104 Saveckaja Street, Gomel 246019, Belarus

doctor of science (physics and mathematics); professor at the department of theoretical physics, faculty of physics and information technologies

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Published
2019-02-10
Keywords: hypersingular integral, Schrödinger equation, momentum space, quadrature formulas
Supporting Agencies This work was supported by the Belarusian Republican Foundation for Fundamental Research (agreement No. Ф17Д-001 dated 06.01.2017). The author is grateful to the Samara University (Russia) for the technical support of numerical calculations in the Wolfram Mathematics system.
How to Cite
Andreev, V. V. (2019). Precision methods for solving the Schrödinger equation with singular potentials in momentum space. Journal of the Belarusian State University. Physics, 1, 97-109. Retrieved from https://journals.bsu.by/index.php/physics/article/view/1387
Issue
No 1 (2019): Journal of the Belarusian State University. Physics
Section
Physics of quantum systems

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