Pseudo-bosons, Riesz bases and coherent states

Details Pseudo-bosons, Riesz bases and coherent states Pseudo-bosons, Riesz bases and coherent states

2010-01-07

arxiv.org/abs/1001.1136v1

Physics

Mathematical Physics

in press in journal of mathematical physics

Scientific paper

In a recent paper, Trifonov suggested a possible explicit model of a PT-symmetric system based on a modification of the canonical commutation relation. Although being rather intriguing, in his treatment many mathematical aspects of the model have just been neglected, making most of the results of that paper purely formal. For this reason we are re-considering the same model and we repeat and extend the same construction paying particular attention to all the subtle mathematical points. From our analysis the crucial role of Riesz bases clearly emerges. We also consider coherent states associated to the model.

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