Open AccessEigenfunction and Green’s function asymptotics for Hill’s equation with symmetric single well potential
Author(s) -
Ayşe Kabataş
Publication year - 2022
Publication title -
ukraïnsʹkij matematičnij žurnal
Language(s) - English
Resource type - Journals
ISSN - 1027-3190
DOI - 10.37863/umzh.v74i2.6246
Subject(s) - eigenfunction , eigenvalues and eigenvectors , mathematics , function (biology) , mathematical analysis , work (physics) , green s , physics , quantum mechanics , evolutionary biology , biology
UDC 517.9This paper is devoted to determine the asymptotic formulae for eigenfunctions of the periodic and semi-periodic Hill's equation when the potential is symmetric single well. The obtained results for eigenvalues by H. Coşkun and the others (2019) are used. With this estimates on the eigenfunctions, Green's functions related to the Hill's equation are obtained. The method is based on the work of C. T. Fulton (1977) to derive Green's functions in an asymptotical manner. We need the derivatives of the solutions in this method. Therefore, the asymptotic approximations for the derivatives of the eigenfunctions are also calculated with different types of restrictions on the potential.