Abstract

ROZO-CLAVIJO, Mauricio. Analysis of a problem of coupled oscillators making use of the bra-ket notation used in quantum mechanics. Rev. acad. colomb. cienc. exact. fis. nat. [online]. 2018, vol.42, n.163, pp.166-171. ISSN 0370-3908.  https://doi.org/10.18257/raccefyn.515.

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.

Keywords : Teaching; Oscillators; Energy; Operator; Eigenvector; Propagator.

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