Examples of pseudo-bosons in quantum mechanics

Examples of pseudo-bosons in quantum mechanics,10.1016/j.physleta.2010.07.044,Physics Letters A,Fabio Bagarello

Examples of pseudo-bosons in quantum mechanics   (Citations: 6)
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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.
Journal: Physics Letters A - PHYS LETT A , vol. 374, no. 37, pp. 3823-3827, 2010
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    • ...In this paper we discuss a two-parameters example of pseudo-bosons, showing, in particular, that they are not regular in the sense of [5]...
    • ...This implies that Sϕ and S� are bounded operators, so that their domains can be taken to be all of H. Particles satisfying Assumptions 1, 2 and 3 are called pseudo-bosons (PB), while if they also satisfy Assumption 4, they are called regular pseudo-bosons (RPB), [5]...
    • ...Remark S�,η extends formally the operator Tθ introduced in [5], where � = 0a ndη was purely imaginary...
    • ...satisfied. As for Assumption 3, the same arguments given in [2 ]a nd [5] apply...

    Fabio Bagarello. Two-Parameters Pseudo-Bosons

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