PERIODIC AND SEMI-PERIODIC EIGENVALUES OF HILL'S EQUATION WITH SYMMETRIC DOUBLE WELL POTENTIAL

PERIODIC AND SEMI-PERIODIC EIGENVALUES OF HILL'S EQUATION WITH SYMMETRIC DOUBLE WELL POTENTIAL

E. Ba┼čkaya

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Abstract

In this paper, some estimates are derived explicitly for periodic and semi-periodic eigenvalues of Hill' s equation with symmetric double well potentials. Also, lengths of the instability intervals are obtained and bounds for the gaps of Dirichlet and Neumann eigenvalues are given by using an auxiliary eigenvalue problem.

Keywords

Hill's equation, symmetric double well potential, periodic and semi-periodic eigenvalues, instability intervals.