Вільний рух частинок у просторі Лобачевського в термінах теорії розсіяння

• Дата: 2019
• Автор: Kurochkin, Yu. A.
• Формат: Стаття
• Мова: English
• Опубліковано: Publishing house "Academperiodika" 2019
• Теми: Lobachevskii space; horosphere; Fourier transform; coordinates; Schr¨odinger equation; scattering; amplitude of scattering; analytical representation; method; iterations; finite differences; -
• Онлайн доступ: https://ujp.bitp.kiev.ua/index.php/ujp/article/view/2019526
• Назва журналу: Ukrainian Journal of Physics

The problem of the motion of a free particle in the three-dimensional Lobachevskii space are interpreted as scattering by the space. The quantum-mechanical case is considered on the basis of the integral equation derived from the Schr¨odinger equation. After the separation of variables in a quasi-Cartesian coordinate system, the integral equation is derived for the momentum component along the axis of symmetry of a horosphere, which coincides with the z axis. The relationship between the scattering amplitude and analytical functions is established. The methods of iteration and finite differences are used to solve the integral equation.