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    題名: Dirac(-Pauli), Fokker-Planck equations and exceptional Laguerre polynomials
    作者: Ho, Choon-Lin
    貢獻者: 淡江大學物理學系
    關鍵詞: Exceptional orthogonal polynomials;Dirac equations;Fokker–Planck equations
    日期: 2011-04
    上傳時間: 2013-04-26 16:40:02 (UTC+8)
    出版者: Maryland Height: Academic Press
    摘要: An interesting discovery in the last two years in the field of mathematical physics has been the exceptional $X_\ell$ Laguerre and Jacobi polynomials. Unlike the well-known classical orthogonal polynomials which start with constant terms, these new polynomials have lowest degree $\ell=1,2,...$, and yet they form complete set with respect to some positive-definite measure. While the mathematical properties of these new $X_\ell$ polynomials deserve further analysis, it is also of interest to see if they play any role in physical systems. In this paper we indicate some physical models in which these new polynomials appear as the main part of the eigenfunctions. The systems we consider include the Dirac equations coupled minimally and non-minimally with some external fields, and the Fokker-Planck equations. The systems presented here have enlarged the number of exactly solvable physical systems known so far.
    關聯: Annals of Physics 326(4), pp.797–807
    DOI: 10.1016/j.aop.2010.12.006
    顯示於類別:[物理學系暨研究所] 期刊論文

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