Classical harmonic oscillator with Dirac-like parameters and possible applications

Details Classical harmonic oscillator with Dirac-like parameters and possible applications Classical harmonic oscillator with Dirac-like parameters and possible applications

2004-02-24

arxiv.org/abs/math-ph/0402065v2

J. Phys. A 37 (2004) 11699-11710

Physics

Mathematical Physics

14 pages, 9 figures, revised, accepted at J. Phys. A

Scientific paper

10.1088/0305-4470/37/48/011

We obtain a class of parametric oscillation modes that we call K-modes with damping and absorption that are connected to the classical harmonic oscillator modes through the "supersymmetric" one-dimensional matrix procedure similar to relationships of the same type between Dirac and Schroedinger equations in particle physics. When a single coupling parameter, denoted by K, is used, it characterizes both the damping and the dissipative features of these modes. Generalizations to several K parameters are also possible and lead to analytical results. If the problem is passed to the physical optics (and/or acoustics) context by switching from the oscillator equation to the corresponding Helmholtz equation, one may hope to detect the K-modes as waveguide modes of specially designed waveguides and/or cavities

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