Journal of Mathematical Physics

The doublet representation of non-Hilbert eigenstates of the Hamiltonian. II

Mario Castagnino, Graciela Domenech, Marcelo Leonardo Levinas, Norberto Umerez

Published Jul 1, 1998• 4 citations

Abstract

Applying the doublet representation we analyze the solutions of a Hamiltonian system which has eigenstates with complex eigenvalues. The example of the Friedrichs model allows us to show how the appearance of solutions with non-Hilbert initial conditions is linked to the energy degeneration of the Hamiltonian spectrum. We discuss the difficulties of giving a physical meaning to the growing or decaying non-Hilbert solutions. We also suggest a way to circumvent the problem of the anomalous probabilities related to both complex energy eigenvalues and degeneration of the spectrum.

DOI: 10.1063/1.532449

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