dorsal/arxiv
View SchemaA new way of defining unstable states
| Authors | Sungyun Kim, Gonzalo Ordonez |
|---|---|
| Categories | |
| ArXiv ID | physics/0311048 |
| URL | https://arxiv.org/abs/physics/0311048 |
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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"abstract": "We define a new unstable state in the Friedrichs model of a two-level atom.\nThis unstable state is a complex eigenstate of the time evolution operator\n$\\exp(-iHt)$ with a restricted test function space, which is obtained from\ncausality conditions. The unstable state shows exact exponential decay for\n$t\\ge0$. Its emitted field is confined inside the future light-cone. In this\nway the long-standing problem of exponential catastrophe is removed. This is an\nexample of quantum mechanics outside Hilbert space, which consists of\ngeneralized eigenstates in a distribution space, and a dual (test function)\nspace.",
"arxiv_id": "physics/0311048",
"authors": [
"Sungyun Kim",
"Gonzalo Ordonez"
],
"categories": [
"physics.atom-ph"
],
"title": "A new way of defining unstable states",
"url": "https://arxiv.org/abs/physics/0311048"
},
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