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

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Communications Faculty of Sciences University Ankara Series A1 Mathematics and Statistics
Volume:71 Issue:3
On eigenfunctions of Hill`s equation with symmetric double well potential

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

Pages : 634-649

View : 12 | Download : 9

Publication Date : 2022-09-30

Article Type : Research Paper

Abstract :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.
Keywords : Hill`s equation, symmetric double well potential, periodic and semi periodic eigenfunctions, Green`s functions, asymptotics

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