Complex Hermite functions as Fourier-Wigner transform

2015/06/23 by Fatima Agorram, Arij Benkhadra, Agorram, Fatima +5
Mathematics · Physics and Astronomy · #33C45 #42C05 #58C40 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Mathematical functions and polynomials #Nonlinear Waves and Solitons #math.CA #msc:33C45 #msc:42C05 #msc:58C40

paper · pdf · doi:10.48550/arxiv.1506.07084

6 pages. Mistakes and misprints are corrected

openalex publication_date 2015/06/23 · arxiv created 2015/07/18 · arxiv updated 2015/07/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the complex Hermite polynomials H_m,n on the complex plane ℂ can be realized as the Fourier-Wigner transform V of the well-known real Hermite functions h_n on real line ℝ. This reduces considerably the Wong's proof giving the explicit expression of V(h_m,h_n) in terms of the Laguerre polynomials. Moreover, we derive a new generating function for the H_m,n as well as some new integral identities.

Citations

• Quantum mechanics as a statistical theory

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