Coupled oscillators, entangled oscillators, and Lorentz-covariant harmonic oscillators
Feb, 2005Citations per year
Abstract: (IOP)
Other than scattering problems where perturbation theory is applicable, there are basicallytwo ways to solve problems in physics. One is to reduce the problem to harmonicoscillators, and the other is to formulate the problem in terms of two-by-two matrices. Iftwo oscillators are coupled, the problem combines both two-by-two matrices and harmonicoscillators. This method then becomes a powerful research tool which can be used in manydifferent branches of physics. Indeed, the concept and methodology in one branch ofphysics can be translated into another through the common mathematical formalism.Coupled oscillators provide clear illustrative examples for some of the currentissues in physics, including entanglement and Feynman's rest of the universe. Inaddition, it is noted that the present form of quantum mechanics is largely aphysics of harmonic oscillators. Special relativity is the physics of the Lorentz groupwhich can be represented by the group of two-by-two matrices commonly calledSL(2,c). Thus the coupled harmonic oscillator can play the role of combining quantummechanics with special relativity. It is therefore possible to relate the currentissues of physics to the Lorentz-covariant formulation of quantum mechanics.Note:
- Typos corrected
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