Stetsko M. One-particle quantum systems in a space with deformed Heisenberg algebra

One-particle quantum problems, namely, the hydrogen atom and the Yukawa potential in deformed space with minimal length were investigated. To obtain the corrections for all levels of the hydrogen atom a modified perturbation theory was developed. The upper bound for the minimal length was obtained. Orbital magnetic moment of an electron in the hydrogen atom in deformed space was investigated. Elastic scattering in deformed space with minimal length was also considered. The general expressions for the scattering amplitude and differential cross-section were found. The scattering amplitudes and differential cross-sections for the Coulomb and Yukawa potential in the Born approximation were calculated. The partial-wave method in deformed space was developed. The results are used in educational process, in scientific work. Application realm is the quantum problems in deformed space.