2016/01/24 by Nicolae Cotfas, Cotfas, Nicolae
Agricultural and Biological Sciences · Computer Science · Mathematics · Physics and Astronomy · #Advanced Computational Techniques in Science and Engineering #Advanced Scientific Research Methods #FOS: Physical sciences #Mathematical Physics (math-ph) #Optical and Acousto-Optic Technologies #Quantum Physics (quant-ph) #math-ph #math.MP #quant-ph
paper · pdf · doi:10.48550/arxiv.1601.06424
Correction: reference to relation (33) replaced with the reference to relation (32) at the end of the proofs of Theorems 3 and 4
openalex publication_date 2016/01/24 · arxiv created 2016/02/17 · arxiv updated 2016/02/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that a new unitary transform with characteristics almost similar to those of the finite Fourier transform can be defined in any finite-dimensional Hilbert space. It is defined by using the Kravchuk polynomials, and we call it Kravchuk transform. Some of its properties are investigated and used in order to obtain a simple alternative description for the irreducible representations of the Lie algebra su(2) and group SU(2). Our approach offers a deeper insight into the structure of the linear representations of SU(2) and new possibilities of computation, very useful in applications in quantum mechanics, quantum information, signal and image processing.