Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 1227.81212
Montesinos, Merced; Torres del Castillo, G.F.
Symplectic quantization, inequivalent quantum theories, and Heisenberg's principle of uncertainty. (English)
[J] Phys. Rev. A (3) 70, No. 3, Article ID 032104, 8 p. (2004). ISSN 1050-2947; ISSN 1094-1622/e

Summary: We analyze the quantum dynamics of the nonrelativistic two-dimensional isotropic harmonic oscillator in Heisenberg's picture. Such a system is taken as a toy model to analyze some of the various quantum theories that can be built from the application of Dirac's quantization rule to the various symplectic structures recently reported for this classical system. It is pointed out that that these quantum theories are inequivalent in the sense that the mean values for the operators (observables) associated with the same physical classical observable do not agree with each other. The inequivalence does not arise from ambiguities in the ordering of operators but from the fact of having several symplectic structures defined with respect to the same set of coordinates. It is also shown that the uncertainty relations between the fundamental observables depend on the particular quantum theory chosen. It is important to emphasize that these (somehow paradoxical) results emerge from the combination of two paradigms: Dirac's quantization rule and the usual Copenhagen interpretation of quantum mechanics.

MSC 2000:: *81S10 Geometric quantization, symplectic methods
53D50 Geometric quantization

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]