Abstract
In this paper, we generalize several results in the article “Analytic continuation of eigenvalues of a quartic oscillator” of A. Eremenko and A. Gabrielov [4].
We consider a family of eigenvalue problems for a Schrödinger equation with even polynomial potentials of arbitrary degree d with complex coefficients, and k < (d + 2)/2 boundary conditions. We show that the spectral determinant in this case consists of two components, containing even and odd eigenvalues respectively.
In the case with k = (d + 2)/2 boundary conditions, we show that the corresponding parameter space consists of infinitely many connected components.
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Alexandersson, P. On Eigenvalues of the Schrödinger Operator with an Even Complex-Valued Polynomial Potential Per Alexandersson. Comput. Methods Funct. Theory 12, 465–481 (2012). https://doi.org/10.1007/BF03321838
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DOI: https://doi.org/10.1007/BF03321838