2013/02/28 by Yoon-Seok Choun, Yoon Seok Choun, Choun, Yoon Seok · 5 citations
Mathematics · Physics and Astronomy · #Mathematical functions and polynomials #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.1302.7309
37 pages, final version. arXiv admin note: text overlap with arXiv:1303.0819, arXiv:1303.0879, arXiv:1303.0813
arxiv created 2014/11/06 · arxiv updated 2014/11/07
In earlier papers [3,4,5,6] Gursey et al. showed development of a bilocal baryon-meson field from two quark-antiquark fields. The Hamiltonian in the case of vanishing quark masses was shown to have a very good agreement with experiments [5]. The theory for vanishing mass was solved using Confluent Hypergeometric functions [6]. In this paper I construct the normalized wave function for the spin-free Hamiltonian with light quark masses (only up to the first order of the mass of quark). I develop the new kind of special function theory in mathematics that generalize all existing theories of Confluent Hypergeometric types. I call it the 'Grand Confluent Hypergeometric (GCH) Function.' My solution produces previously unknown extra "hidden" radial quantum numbers relevant for description of supersymmetry and for generating new mass formulas. This paper is 1st out of 10 in series "Special functions and three term recurrence formula (3TRF)". See section 6 for all the papers in the series. The next paper in the series describes generalization of three term recurrence relation in linear ordinary differential equations and its applications [8].