Geodesic
Dissipation evidence for the~quantum damped harmonic oscillator via pseudo-bosons
Teoretičeskaâ i matematičeskaâ fizika, Tome 171 (2012) no. 1, pp. 87-95

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It is known that a self-adjoint, time-independent Hamiltonian can be defined for the quantum damped harmonic oscillator. We show that the two vacuums naturally associated with this operator seem to be non-square-integrable when it is expressed in terms of pseudo-bosonic lowering and raising operators. This fact is interpreted as the evidence of a dissipation effect of the classical oscillator on a purely quantum level.
Keywords: quantum harmonic oscillator
Mots-clés : pseudo-boson. 
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     author = {F. Bagarello},
     title = {Dissipation evidence for the~quantum damped harmonic oscillator via pseudo-bosons},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {87--95},
     publisher = {mathdoc},
     volume = {171},
     number = {1},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2012_171_1_a7/}
}
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F. Bagarello. Dissipation evidence for the~quantum damped harmonic oscillator via pseudo-bosons. Teoretičeskaâ i matematičeskaâ fizika, Tome 171 (2012) no. 1, pp. 87-95. http://geodesic.mathdoc.fr/item/TMF_2012_171_1_a7/