Abstract
The existence of particle outflow in the decay of many-body system leads to a special description with two sets of state eigenvectors and corresponding complex eigenvalues. Using such eigenvectors the general time behavior of the decaying system is obtained. As an example, we consider the problem of a particle decay of the many-body system to demonstrate the difference between this problem and the problem of a single particle in potential well. We also consider the case of particle scattering by an optical potential and show that the existence of outflow also leads to two sets of state eigenvectors, but with real energy eigenvalues.
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