The Analytic Properties of the S-matrix for Arbitrary Interactions Which Externally Pass into the Centrifugal and Rapidly Decreasing Potentials

• Дата: 2010
• Автор: Olkhovsky, V.S.
• Формат: Стаття
• Мова: English
• Опубліковано: Відділення фізики і астрономії НАН України 2010
• Назва видання: Український фізичний журнал
• Теми: Загальні питання теоретичної фізики
• Онлайн доступ: http://dspace.nbuv.gov.ua/handle/123456789/56200
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Цитувати: The Analytic Properties of the S-matrix for Arbitrary Interactions Which Externally Pass into the Centrifugal and Rapidly Decreasing Potentials / V.S. Olkhovsky // Український фізичний журнал. — 2010. — Т. 55, № 5. — С. 568-578. — Бібліогр.: 32 назв. — англ.

The analytic structure of non-relativistic unitary and non-unitary S-matrices is reviewed for the cases of arbitrary interactions (and may be, with the unspecified equations of motion) inside a sphere of radius r ≤ a which pass outside it (at r > a) into the centrifugal and decreasing (exponentially, by the Yukawa law, or more rapidly) potentials on the base of the author’s papers from 1961 till 2006. The one-channel case and special examples of many-channel cases are considered. Some kinds of the symmetry conditions are imposed. The Schr¨odinger equation for r > a for the particle motion and the condition of completeness of the corresponding wave functions are assumed. Finally, a scientific program of the future research is presented as a clear continuation and an extension of the obtained results.