arXiv:quant-ph/0603259AbstractReferencesReviewsResources
Comment on ``Symplectic quantization, inequivalent quantum theories, and Heisenberg's principle of uncertainty''
Published 2006-03-28, updated 2007-01-08Version 2
In Phys. Rev. A 70, 032104 (2004), M. Montesinos and G. F. Torres del Castillo consider various symplectic structures on the classical phase space of the two-dimensional isotropic harmonic oscillator. Using Dirac's quantization condition, the authors investigate how these alternative symplectic forms affect this system's quantization. They claim that these symplectic structures result in mutually inequivalent quantum theories. In fact, we show here that there exists a unitary map between the two representation spaces so that the various quantizations are equivalent.
Comments: 6 pages, updated version
Journal: Phys. Rev. A 75, 066101 (2007)
Categories: quant-ph
Keywords: heisenbergs principle, symplectic quantization, uncertainty, two-dimensional isotropic harmonic oscillator, symplectic structures result
Tags: journal article
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Symplectic quantization, inequivalent quantum theories, and Heisenberg's principle of uncertainty