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- W1987726265 abstract "A type of nonhomogeneous integral equation frequently encountered in interaction problems is solved by means of the Heaviside expansion theorem. The energy spectrum is obtained in the usual way from the solutions of the dispersion equation for the excitations, D(k, s) = 0. The momentum spectrum is obtained as the solutions of ∂D/∂k = 0, which is shown to be also a form of the Cauchy-Riemann equations. It is proved that the existence of a solution of ∂D/∂k = 0 is a necessary condition for the existence of an analytic region on the momentum plane. It is also proved that the existence of a solution of dD/dk = 0 and ∂D/∂s = 0 is a necessary and sufficient condition for the existence of analytic regions in both variables, provided the group velocity is finite and continuous. As an example, two linearized self-consistent equations with arbitrary coupling are solved." @default.
- W1987726265 created "2016-06-24" @default.
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- W1987726265 date "1967-05-01" @default.
- W1987726265 modified "2023-10-18" @default.
- W1987726265 title "Complete Excitation Spectra" @default.
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- W1987726265 doi "https://doi.org/10.1063/1.1705334" @default.
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