Quantization of classical lagrangian mechanics
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The equations of motion of a massive rigid body in the Lagrange—Poisson case (when one point of the body is fixed) are expressed in Hamiltonian form, making it possible to describe the Lagrangian rigid body in terms of classical mechanics. Using Berezin's quantization algorithm, it is possible to associate the Lagrangian classical mechanics with a quantum system, namely, a system of two-level particles interacting with a resonant field.
KeywordsRigid Body Quantum System Classical Mechanic Hamiltonian Form Quantization Algorithm
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- 1.V. V. Golubev,Lectures on Integration of the Equations of Motion of a Massive Rigid Body About a Fixed Point [in Russian], GITTL, Moscow (1973).Google Scholar
- 2.F. A. Berezin,The Method of Second Quantization, New York (1966).Google Scholar
- 3.P. Olver,Applications of Lie Groups to Differential Equations [Russian translation], Mir, Moscow (1989).Google Scholar
- 4.A. M. Perelomov,Generalized Coherent States and Their Applications, [in Russian], Nauka, Moscow (1987).Google Scholar
- 5.A. M. Kirillov, “Geometric quantization,” in:Modern Problems of Mathematics, Reviews of Science and Technology, Vol. 4 [in Russian], All-Union Institute of Scientific and Technical Information (VINITI), Moscow (1985).Google Scholar
- 6.E. I. Bogdanov,Teor. Mat. Fiz.,72, 244 (1987).Google Scholar
- 7.N. Y. Vilenkin,Special Functions and the Theory of Group Representations, AMS Translations of Math Monogr., Vol. 22, Providence, R.I. (1968).Google Scholar