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Foundations of Physics

Non-Heisenberg states of the harmonic oscillator

K. Dechoum, H. M. França

Published Nov 1, 1995• 11 citations
Publisher
DOI
10.1007/bf02055510

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The polynomial Heisenberg algebras (PHA) are deformations of the Heisenberg- Weyl algebra characterizing the underlying symmetry of the supersymmetric partners of the Harmonic oscillator. When looking for the simplest system ruled by PHA, however, we end up with the harmonic oscillator. In this paper we are going to realize the first-order PHA through the harmonic oscillator. The associated coherent states will be also constructed, which turn out to be the well known even and odd coherent states.
Abstract The equilibrium properties of an open harmonic oscillator are considered in three steps: first the creation and destruction operators are generalized for open dynamics and the creation operator is used to construct coherent states. The second step consists of the introduction of the Heisenberg representation where the dynamical decoherence is identified. Finally it is pointed out that the quantum fluctuations generate non-continuous limit for infinitesimal system–environment interactions and at the border of the under- and over-damped oscillator.