2013/10/04 by Won Sang Chung, Chung, Won Sang, Mahouton Norbert Hounkonnou +3
Mathematics · Physics and Astronomy · #33D45 #FOS: Physical sciences #Mathematical Physics (math-ph) #Mathematical functions and polynomials #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics
paper · pdf · doi:10.48550/arxiv.1310.1280
openalex publication_date 2013/10/04 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28
This paper addresses a construction of new q-Hermite polynomials with a full characterization of their main properties and corresponding raising and lowering operator algebra. The three-term recursive relation as well as the second-order differential equation obeyed by these new polynomials are explicitly derived. Relevant operator actions, including the eigenvalue problem of the deformed oscillator and the self-adjointness of the related position and momentum operators, are investigated and analyzed. The associated coherent states are constructed and discussed with an explicit resolution of the induced moment problem.