We discuss two physical examples of the so-called pseudo-bosons, recently introduced in connection with pseudo-hermitian quantum mechanics. In particular, we show that the so-called extended harmonic oscillator and the Swanson model satisfy all the assumptions of the pseudo-bosonic framework introduced by the author. We also prove that the biorthogonal bases they produce are not Riesz bases.
Bagarello, F. (2010). Examples of pseudo-bosons in quantum mechanics. PHYSICS LETTERS A, 374(37), 3823-3827 [10.1016/j.physleta.2010.07.044].
Examples of pseudo-bosons in quantum mechanics
BAGARELLO, Fabio
2010-01-01
Abstract
We discuss two physical examples of the so-called pseudo-bosons, recently introduced in connection with pseudo-hermitian quantum mechanics. In particular, we show that the so-called extended harmonic oscillator and the Swanson model satisfy all the assumptions of the pseudo-bosonic framework introduced by the author. We also prove that the biorthogonal bases they produce are not Riesz bases.
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