Quantization of the Kepler manifold

Cordani, Bruno

doi:10.1007/bf01223241

Cited by 5 publications

(1 citation statement)

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“…Methods of GQ have been applied with great success to the theory of representation of Lie groups [11], however, its usefulness in applications to quantum theory has been rather limited. At least in this terms the cornerstones of quantum mechanics, the harmonic oscillator and the hydrogen atom, GQ gives results in agreement with those of CQ [9,[12][13][14][15][16]. The geometric quantization achievements are still under those accomplished by canonical quantization.…”

Section: Introductionmentioning

confidence: 65%

Remarks on the geometric quantization of a class of harmonic oscillator type potentials

Iacob¹

2016

Preprint

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The conditions that must be fulfilled by a certain physical system to apply geometric quantization prescription on it are investigated. These terms are sought as mathematical requirements, which can be traced in an analysis of integrable systems, from the perspective of both potential function and Hamiltonian vector field. The answer is found in momentum map critical points. Basically, a certain disposal of points that allow a momentum map C * isomorphism, of observables, with harmonic oscillator momentum map enforce geometric quantization rules.Following the general theory, two newly presented examples, which exhibits these properties, are quantified through geometric quantization prescription. The Lennard-Jones' type potential is one of the examples, it is known as describing molecules in interaction. We end with a third example that shows the local isomorphism of potentials do not induce C * isomorphism of observables.

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