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

Kabataş A.

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

  • 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.