Application of approximate symmetries to the construction of solutions of classical and quantum Hamiltonian systems

Abstract

A method for integration of classical and quantum Hamiltonian systems, based on the use of approximate symmetries, is proposed in this paper. The proposed method is similar to the averaging method in classical mechanics; however, it does not use canonical transformations to the variables "action-angle." This allows one in some cases to apply this method to quantum equations. A nontrivial example is analyzed in the paper.

Original language	English
Pages (from-to)	806-808
Number of pages	3
Journal	Russian Physics Journal
Volume	36
Issue number	8
DOIs	https://doi.org/10.1007/BF00562038
Publication status	Published - Aug 1993
Externally published	Yes

ASJC Scopus subject areas

Physics and Astronomy(all)

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10.1007/BF00562038

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title = "Application of approximate symmetries to the construction of solutions of classical and quantum Hamiltonian systems",

abstract = "A method for integration of classical and quantum Hamiltonian systems, based on the use of approximate symmetries, is proposed in this paper. The proposed method is similar to the averaging method in classical mechanics; however, it does not use canonical transformations to the variables {"}action-angle.{"} This allows one in some cases to apply this method to quantum equations. A nontrivial example is analyzed in the paper.",

author = "Shapovalov, {A. V.} and Shirokov, {I. V.}",

year = "1993",

month = aug,

doi = "10.1007/BF00562038",

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pages = "806--808",

journal = "Russian Physics Journal",

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AB - A method for integration of classical and quantum Hamiltonian systems, based on the use of approximate symmetries, is proposed in this paper. The proposed method is similar to the averaging method in classical mechanics; however, it does not use canonical transformations to the variables "action-angle." This allows one in some cases to apply this method to quantum equations. A nontrivial example is analyzed in the paper.

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Application of approximate symmetries to the construction of solutions of classical and quantum Hamiltonian systems

Abstract

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