Email this article The oscillator's model with broken symmetry
- Authors: Volov D.B1
-
Affiliations:
- Samara State Transport University
- Issue: Vol 19, No 4 (2015)
- Pages: 624-633
- Section: Articles
- URL: https://journal-vniispk.ru/1991-8615/article/view/20445
- DOI: https://doi.org/10.14498/vsgtu1379
- ID: 20445
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Abstract
The equations of the oscillator motion are considered. The exact solutions are given in the form of exponents with an additional parameter that characterizes the asymmetry of the oscillations. It is shown that these equations are the special case of the Hill’s equation. The equations for the three types of exponents, including having the property of unitarity are obtained. Lagrangians and Hamiltonians are found for these equations. It is proved that all the equations are associated by canonical transformations and essentially are the same single equation, expressed in different generalized coordinates and momenta. Moreover, the solutions of linear homogeneous equations of the same type are both solutions of inhomogeneous linear equations of another one. A quantization possibility of such systems is discussed.
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##article.viewOnOriginalSite##About the authors
Dmitry B Volov
Samara State Transport University
Email: volovdm@mail.ru
(Dr. Tech. Sci.; volovdm@mail.ru), Professor, Dept. of Physics and Chemistry 18, First Bezimyanniy per., Samara, 443066, Russian Federation
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