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arXiv · 1010.4221

Modified Landau levels, damped harmonic oscillator and two-dimensional pseudo-bosons

Syed Twareque Ali·Fabio Bagarello·Jean-Pierre Gazeau
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Abstract

In a series of recent papers one of us has analyzed in some details a class of elementary excitations called {\em pseudo-bosons}. They arise from a special deformation of the canonical commutation relation $[a,a^\dagger]=\1$, which is replaced by $[a,b]=\1$, with $b$ not necessarily equal to $a^\dagger$. Here, after a two-dimensional extension of the general framework, we apply the theory to a generalized version of the two-dimensional Hamiltonian describing Landau levels. Moreover, for this system, we discuss coherent states and we deduce a resolution of the identity. We also consider a different class of examples arising from a classical system, i.e. a damped harmonic oscillator.

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Syed Twareque Ali, Fabio Bagarello, Jean-Pierre Gazeau. 2010-10-20. Modified Landau levels, damped harmonic oscillator and two-dimensional pseudo-bosons. https://arxiv.org/abs/1010.4221

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