Quantization of Hamiltonian and non-Hamiltonian systemsстатьяИсследовательская статья
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Дата последнего поиска статьи во внешних источниках: 26 января 2024 г.
Аннотация:The quantization process was always tightly connected to the Hamiltonian formulation ofclassical mechanics. For non-Hamiltonian systems, traditional quantization algorithms turn out to beunsuitable. Numerous attempts to quantize non-Hamiltonian systems have shown that this problem is nontrivial and requires the development of new approaches. In this paper, we present the quantization methods that do not depend upon the Hamiltonian formulation of classical mechanics. Two approaches to the quantization of mechanical systems are considered: axiomatic and hydrodynamic. It is shown that the formal application of these approaches to the classical Hamilton-Jacobi theory allows obtaining the wave equation for the corresponding quantum system in natural way. Examples are considered that show the effectiveness of the proposed approaches, both for Hamiltonian and nonHamiltonian systems. The spinor form of the relativistic Hamilton-Jacobi theory for classical particles is considered. It is shown that it naturally leads to the Dirac equation for the corresponding quantum particle and to its non-Hamiltonian generalization, the bispinor relativistic Kostin equation.