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Интеллектуальная Система Тематического Исследования НАукометрических данных |
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Fall of a Particle to the Center of a Singular Potential: Classical vs. Quantum Exact Solutionsстатья
- Автор: Tribelsky Michael I.
- Журнал: ArXiv e-prints
- Год издания: 2022
- DOI: 10.48550/ARXIV.2202.12615
- Аннотация: Exact solutions describing a fall of a particle to the center of a singular potential (collapse) in classical and quantum cases are obtained, inspected, and compared. The solutions exhibit striking similarities. In particular, at zero energy of the particle, both are self-similar, and their characteristic spatial scales obey the same temporal dependence. In addition to collapsing, exact expanding solutions, corresponding to the escape of the particle from the singularity, exist for both problems too. The collapse and escape are independent and not linked to each other through the singularity. In the quantum collapse, the wave functions of the exact solutions have time-depended norms. It requires to perform reconsideration and generalization for this case the continuity equations and rules for mean value calculations. The analysis sheds new light on the fundamentals of quantum mechanics.
- Добавил в систему: Трибельский Михаил Исаакович