On eigenfunctions of Hill's equation with symmetric double well potential

Kabataş, AYŞE

doi:10.31801/cfsuasmas.974409

On eigenfunctions of Hill's equation with symmetric double well potential

COMMUNICATIONS FACULTY OF SCIENCES UNIVERSITY OF ANKARA-SERIES A1 MATHEMATICS AND STATISTICS, cilt.71, sa.3, ss.634-649, 2022 (ESCI, TRDizin)

Yayın Türü: Makale / Tam Makale
Cilt numarası: 71 Sayı: 3
Basım Tarihi: 2022
Doi Numarası: 10.31801/cfsuasmas.974409
Dergi Adı: COMMUNICATIONS FACULTY OF SCIENCES UNIVERSITY OF ANKARA-SERIES A1 MATHEMATICS AND STATISTICS
Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), TR DİZİN (ULAKBİM)
Sayfa Sayıları: ss.634-649
Anahtar Kelimeler: &nbsp, Hill&rsquo, s equation, symmetric double well potential, periodic and semi-periodic eigen-functions, Green?s functions, asymptotics, EIGENVALUE PARAMETER, SPECTRUM
Karadeniz Teknik Üniversitesi Adresli: Evet

Özet

Throughout this paper the asymptotic approximations for eigen- functions of eigenvalue problems associated with Hill’s equation satisfying periodic and semi-periodic boundary conditions are derived when the potential is symmetric double well. These approximations are used to determine the Green’s functions of the related problems. Then, the obtained results are adapted to the Whittaker-Hill equation which has the symmetric double well potential and is widely investigated in the literature.