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arXiv · 1305.0514

Pseudo-bosons for the $D_2$ type quantum Calogero model

Fabio Bagarello
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Abstract

In the first part of this paper we show how a simple system, a 2-dimensional quantum harmonic oscillator, can be described in terms of pseudo-bosonic variables. This apparently {\em strange} choice is useful when the {\em natural} Hilbert space of the system, $L^2({\bf R}^2)$ in this case, is, for some reason, not the most appropriate. This is exactly what happens for the $D_2$ type quantum Calogero model considered in the second part of the paper, where the Hilbert space $L^2({\bf R}^2)$ appears to be an unappropriate choice, since the eigenvectors of the relevant hamiltonian are not square-integrable. Then we discuss how a certain intertwining operator arising from the model can be used to fix a different Hilbert space more {\em useful}.

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Fabio Bagarello. 2013-05-02. Pseudo-bosons for the $D_2$ type quantum Calogero model. https://arxiv.org/abs/1305.0514

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