We consider a -Symmetric Hamiltonian System of differential equations on a half interval or the real line. We determine the spectrum and construct the resolvent for the system. The essential spectrum is found to be a subset of an algebraic curve defined by a characteristic polynomial for the system. The results are first proved for a constant coefficient system and then for an almost constant coefficient system. The results are applied to a number of examples including the complex hydrogen atomand the complex relativistic electron.
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Horst Behncke, Don B. Hinton, -symmetric Hamiltonian systems with almost constant coefficients. J. Spectr. Theory 9 (2019), no. 2, pp. 513–546DOI 10.4171/JST/254