Abstract
The Riemann sheet structure of the energy levels E n(λ) of an N-dimensional symmetric matrix problem of the form H 0 + λH 1 is discussed. It is shown that the singularities of the energy levels in the complex λ-plane are related to avoided level crossings. In the vicinity of a complex conjugate pair of exceptional points the full matrix problem behaves locally like a two dimensional problem. The significance of the exceptional points for the non-linear system of differential equations which determine the energy levels and state vectors as functions of λ is discussed.
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