2D-Zernike polynomials and coherent state quantization of the unit disc

2013/03/21 by K. Thirulogasanthar, Nasser Saad, Thirulogasanthar, K. +3 · 1 citation
Mathematics · Physics and Astronomy · #46E22 #81R15 #81R30 #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP #msc:46E22 #msc:81R15 #msc:81R30

paper · pdf · doi:10.48550/arxiv.1303.5483

15 pages In Mathematical Physics, Analysis and Geometry, Jan. 7, 2015

arxiv created 2015/01/07 · arxiv updated 2015/01/08

Abstract

Using the orthonormality of the 2D-Zernike polynomials, reproducing kernels, reproducing kernel Hilbert spaces, and ensuring coherent states attained. With the aid of the so-obtained coherent states, the complex unit disc is quantized. Associated upper symbols, lower symbols and related generalized Berezin transforms also obtained. A number of necessary summation formulas for the 2D-Zernike polynomials proved.

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• Zernike polynomials from the tridiagonalization of the radial harmonic oscillator in displaced Fock states

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