How to Cite
Downloads
Most read articles by the same author(s)
- Mauricio Rozo Clavijo, On the dynamics of a rotating particle using the concept of gauge invariance , Revista de la Academia Colombiana de Ciencias Exactas, Físicas y Naturales: Vol. 40 No. 157 (2016)
Métricas Alternativas
Dimensions
Abstract
A detailed analysis is performed on a system consisting of four oscillators coupled with different mass and coupling constant. The dynamics is obtained from the analysis governing the behavior of the system from the perspective of a classical context, and also using concepts of linear algebra and the bra-ket notation used in quantum mechanics. In this context, the solution for the oscillators system is obtained by making use of a standard base generated from of the initial position for each oscillator, which allows to establish a well-defined state that is interpreted as the displacement of the oscillator with respect to its position of equilibrium. In this order of ideas, the equations of motion are decoupled through a similarity transformation constructed from a set of eigenvectors to obtain the solution. This strategy offers the possibility of evidencing the temporal evolution of the system of oscillators by means of an operator identified with the propagator of the state of the system. Such analysis is important as it is novel and it generates an alternative, didactic and robust way of approaching this issue by connecting it with a known topic of classical mechanics. In addition, it allows students to familiarize themselves with the bra-ket notation and the procedures used to solve problems in quantum mechanics, such as the problem of eigenvalues. © 2018. Acad. Colomb. Cienc. Ex. Fis. Nat.References
Bronson, R. Costa, G. (1991). Matrix Methods, Academic Press, INC, San Diego, 175-194.
Crawford, F. S. (1994). Berkeley Physics Course Ondas, Reverté S.A. España, 2-31.
Dirac, P. A. M. (1968). Principio de Mecánica Cuántica, Ediciones Ariel, España, 15-17.
Feynman, R. (1964). The Feynman lectures on Physics, Vol III. Addison- Wesley Publishing Company, Masachusetts, E.U.A, 5-17.
French, A. P. (1974). Vibraciones y Ondas, Editorial Reverté S. A, España, 227-257.
Gillespie, D. (1991). Introducción a la mecánica cuántica, Editorial Reverté S. A, España, 60-80.
Grossman, S. Flores, J. J. (2012). Algebra lineal, McGraw-Hill, México, 564-572.
Herrmann, F. Schmälzle, P. (1981). Simple explanation of a wellknown collision experiment, Am. J. Phys. 49: 761-764.
Marion J. B. (1992). Dinámica Clásica de las Partículas y Sistemas, Reverté S.A. España, 103-120.
Real Academia Española. (2017). Fecha de consulta: 8 de mayo de 2018. Disponible en: http://buscon.rae.es/draeI/SrvltConsulta?TIPO_BUS=3&LEMA=estado
Rozo M. (2016). Sobre la dinámica de una partícula en rotación usando el concepto de invariancia gauge. Revista de la Academia Colombiana de Ciencias Exactas, Físicas y Naturales. 40 (157): 585-589.
Schmid, G. B. (1983). An up to date approach to physics, Am. J. Phys. 52, (9): 794-799.
Sposito, G. (1976). Introduction to Classical Dynamics, John Wiley and Sons, U.S.A, 37-46.
Symon, K. (1968). Mecánica. Addison-Wesley, España, 194-204.
Towmsend, J. (2000). A modern Approach to Quantum Mechanics, University Science Books, California, 93-111.
Declaration of originality and transfer author's rights
The authors declare:
- The published data and reference materials have been duly identified with their respective credits and have been included in the bibliographic notes and citations that have been so identified and that should it be required, I have all releases and permissions from any copyrighted material.
- All material presented is free from any copyright and that I accept full legal responsibility for any legal claims relating to copyrighted intellectual property, fully exonerating from responsibility the Revista de la Academia Colombiana de Ciencias Exactas, Físicas y Naturales.
- This work is unpublished and will not be sent to any other journal while waiting for the editorial decision of this journal. I declare that there is no conflict of interest in this manuscript.
- In case of publication of this article, all author´s rights are transferred to the Revista de la Academia Colombiana de Ciencias Exactas, Físicas y Naturales, and so cannot be reproduced in any form without the express permission of it.
- By means of this document, if the article is accepted for publication by the Revista de la Academia Colombiana de Ciencias Exactas, Físicas y Naturales, the Revista assumes the right to edit and publish the articles in national and international indices or data bases for academic and scientific use in paper, electronic, CD-ROM, internet form either of the complete text or any other known form known or to be known and non-commercial, respecting the rights of the authors.
Transfer of author rights
In case the article is approved for publication, the main author in representation of himself and his co-authors or the main author and his co-authors must cede the author rights of the corresponding article to the Revista de la Academia Colombiana de Ciencias Exactas, Físicas y Naturales, except in the following cases:
The authors and co-authors will retain the right to revise, adapt, prepare derived works, oral presentations, and distribution to some colleagues of reprints of their own published work, if the corresponding credit is given to the Revista de la Academia Colombiana de Ciencias Exactas, Físicas y Naturales. It is also permissible to publish the title of the work, summary, tables, and figures of the work in the corresponding web sites of the authors or their employers, also giving credit to the Revista.
If the work has been realized under contract, the author’s employer has the right to revise, adapt, prepare derivative works, reproduce, or distribute in hard copy the published work, in a secure manner and for the exclusive use of his employees.
If the Revista de la Academia Colombiana de Ciencias Exactas, Físicas y Naturales were approached for permission by a third party for using, printing, or publishing specifically articles already published, the Revista must obtain the express permission of the author and co-authors of the work or of the employer except for use in classrooms, libraries, or reprinted in a collective work. The Revista de la Academia Colombiana de Ciencias Exactas, Físicas y Naturales reserves the possible use in its front cover of figures submitted with the manuscripts.
No other right, other than the author’s right, can be claimed by the Revista de la Academia Colombiana de Ciencias Exactas, Físicas y Naturales.