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Keywords
(4)
Harmonic Oscillator
Quantum Mechanics
riesz bases
Satisfiability
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Examples of pseudobosons in quantum mechanics
Examples of pseudobosons in quantum mechanics,10.1016/j.physleta.2010.07.044,Physics Letters A,Fabio Bagarello
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Examples of pseudobosons in quantum mechanics
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Citations: 6
)
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Fabio Bagarello
We discuss two physical examples of the socalled pseudobosons, recently introduced in connection with pseudohermitian quantum mechanics. In particular, we show that the socalled extended
harmonic oscillator
and the Swanson model satisfy all the assumptions of the pseudobosonic 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. 38233827, 2010
DOI:
10.1016/j.physleta.2010.07.044
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Citation Context
(1)
...In this paper we discuss a twoparameters example of pseudobosons, 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 pseudobosons (PB), while if they also satisfy Assumption 4, they are called regular pseudobosons (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
.
TwoParameters PseudoBosons
References
(10)
Pseudobosons, Riesz bases, and coherent states
(
Citations: 8
)
Fabio Bagarello
Journal:
Journal of Mathematical Physics  J MATH PHYSNY
, vol. 51, no. 2, pp. 3531023531, 2010
Construction of pseudobosons systems
(
Citations: 6
)
Fabio Bagarello
Published in 2010.
Mathematical aspects of intertwining operators: the role of Riesz bases
(
Citations: 4
)
Fabio Bagarello
Journal:
Journal of Physics Amathematical and Theoretical  J PHYS AMATH THEOR
, vol. 43, no. 17, 2010
On pseudoHermitian Hamiltonians and their Hermitian counterparts
(
Citations: 20
)
H. F. Jones
Journal:
Journal of Physics Amathematical and General  J PHYSAMATH GEN
, vol. 38, no. 8, pp. 17411746, 2005
An Introduction to Nonharmonic Fourier Series
(
Citations: 528
)
R. Young
Published in 2001.
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Citations
(6)
TwoParameters PseudoBosons
(
Citations: 1
)
Fabio Bagarello
Journal:
International Journal of Theoretical Physics  INT J THEOR PHYS
, vol. 50, no. 4, pp. 10601065, 2011
Weak commutation relations of unbounded operators and applications
Fabio Bagarello
,
Atsushi Inoue
,
Camillo Trapani
Published in 2011.
Pseudobosons arising from standard ladder operators
Fabio F. G. Calabrese
Published in 2011.
A Note on the PaisUhlenbeck Model and Its Coherent States
F. Bagarello
Journal:
International Journal of Theoretical Physics  INT J THEOR PHYS
, vol. 50, pp. 110, 2011
Modified Landau levels, damped harmonic oscillator and twodimensional pseudobosons
(
Citations: 3
)
Syed Twareque Ali
,
Fabio Bagarello
,
JeanPierre Gazeau
Published in 2010.