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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2011
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/1102.0990 |
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Table des matières:
- For the Caldirola-Kanai system, describing a quantum damped harmonic oscillator, a couple of constant-of-motion operators generating the Heisenberg algebra can be found. The inclusion of the standard time evolution symmetry in this algebra for damped systems, in a unitary manner, requires a non-trivial extension of this basic algebra and hence the physical system itself. Surprisingly, this extension leads directly to the so-called Bateman's dual system, which now includes a new particle acting as an energy reservoir. The group of symmetries of the dual system is presented, as well as a quantization that implies, in particular, a first-order Schrödinger equation. The usual second-order equation and the inclusion of the original Caldirola-Kanai model in Bateman's system are also discussed.