Abstract
The Riemann sheet structure of the energy levels En(λ) of an N-dimensional symmetric matrix problem of the form H0+λH1 is discussed. It is shown that the singularities of the energy levels in the complex λ plane are related to avoided level crossings. It is argued that locally the sheet structure is like that of a two-, three-, or four-dimensional problem as far as two, three, or four adjacent levels are concerned. Expressions are given for adjacent levels displaying explicitly the Riemann sheet structure on a semiglobal footing.
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