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DOE OSTI · 22220717

Quantizations from reproducing kernel spaces

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Abstract

The purpose of this work is to explore the existence and properties of reproducing kernel Hilbert subspaces of L{sup 2}(C,d{sup 2}z/π) based on subsets of complex Hermite polynomials. The resulting coherent states (CS) form a family depending on a nonnegative parameter s. We examine some interesting issues, mainly related to CS quantization, like the existence of the usual harmonic oscillator spectrum despite the absence of canonical commutation rules. The question of mathematical and physical equivalences between the s-dependent quantizations is also considered. -- Highlights: ► We discuss in detail an interesting decomposition of L{sup 2}, in terms of ladder operators. ► We consider coherent states on this structure and we use them for quantization. ► We show how this structure is related with non hermitian quantum mechanics. ► We consider the relation between different schemes of quantizations.

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71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICSANNIHILATION OPERATORSDECOMPOSITIONEIGENSTATESHARMONIC OSCILLATORSHERMITE POLYNOMIALSKERNELSQUANTIZATIONQUANTUM MECHANICSSPACE

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2013-05-15. Quantizations from reproducing kernel spaces. https://doi.org/10.1016/j.aop.2013.02.004

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