A new way of defining unstable states

Sungyun Kim; Gonzalo Ordonez

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A new way of defining unstable states

Sungyun Kim·Gonzalo Ordonez

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Abstract

We define a new unstable state in the Friedrichs model of a two-level atom. This unstable state is a complex eigenstate of the time evolution operator $\exp(-iHt)$ with a restricted test function space, which is obtained from causality conditions. The unstable state shows exact exponential decay for $t\ge0$. Its emitted field is confined inside the future light-cone. In this way the long-standing problem of exponential catastrophe is removed. This is an example of quantum mechanics outside Hilbert space, which consists of generalized eigenstates in a distribution space, and a dual (test function) space.

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Sungyun Kim, Gonzalo Ordonez. 2005-07-05. A new way of defining unstable states. https://arxiv.org/abs/physics/0311048

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