Exact solutions to fall of particle to singular potential: Classical versus quantum cases

Tribelsky, M.I.

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Дата последнего поиска статьи во внешних источниках: 20 февраля 2024 г.

Автор: Tribelsky Michael I.
Журнал: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Том: 479
Номер: 2278
Год издания: 2023
Издательство: Royal Society of London
Местоположение издательства: United Kingdom
Первая страница: 2
Последняя страница: 22
DOI: 10.1098/rspa.2023.0366
Аннотация: Exact solutions describing a fall of a particle to the center of a non-regularized singular potential in classical and quantum cases are obtained and compared. We inspect the quantum problem with the help of conventional Schr\"{o}dinger's equation. During the fall, the wave function spatial localization area contracts into a single zero-dimensional point. For the fall-admitting potentials, the Hamiltonian is non-Hermitian. Because of that, the wave function norm occurs time-depended. It demands an extension to this case of the continuity equation and rules for mean value calculations. Surprisingly, the quantum and classical solutions exhibit striking similarities. In particular, both are self-similar at the particle energy equals zero. The characteristic spatial scales of the quantum and classical self-similar solutions obey the same temporal dependence. We present arguments indicating that these self-similar solutions are attractors to a broader class of solutions, describing the fall at finite energy of the particle.
Добавил в систему: Трибельский Михаил Исаакович

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Exact solutions to fall of particle to singular potential: Classical versus quantum casesстатья

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