2015/12/08 by Nicolae Cotfas, Cotfas, Nicolae
Computer Science · Mathematics · Physics and Astronomy · #81Q35 #Digital Filter Design and Implementation #FOS: Physical sciences #Image and Signal Denoising Methods #Mathematical Analysis and Transform Methods #Mathematical Physics (math-ph) #Quantum Physics (quant-ph) #math-ph #math.MP #msc:81Q35 #quant-ph
paper · pdf · doi:10.48550/arxiv.1512.02589
23 pages, 6 figures
arxiv created 2015/12/08 · openalex publication_date 2015/12/08 · arxiv updated 2015/12/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The mathematical description of the quantum harmonic oscillator is essentially based on the Gaussian function. In the case of a quantum oscillator with finite-dimensional Hilbert space, the position space consists in a finite number of points, and the ground state can be regarded as a finite version of the Gaussian function. Conversely, each finite Gaussian can be used in order to define some finite oscillators. We investigate certain finite Gaussians as concern their Fourier transform, Wigner function and associated oscillators.