We show how the notion of pseudo-bosons, originally introduced as operators acting on some Hilbert space, can be extended to a distributional settings. In doing so, we are able to construct a rather general framework to deal with generalized eigenvectors of the multiplication and of the derivation operators. Connections with the quantum damped harmonic oscillator are also briefly considered.
Bagarello F. (2020). Weak pseudo-bosons. JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL, 53(13), 135201 [10.1088/1751-8121/ab766f].
Weak pseudo-bosons
Bagarello F.
2020-01-01
Abstract
We show how the notion of pseudo-bosons, originally introduced as operators acting on some Hilbert space, can be extended to a distributional settings. In doing so, we are able to construct a rather general framework to deal with generalized eigenvectors of the multiplication and of the derivation operators. Connections with the quantum damped harmonic oscillator are also briefly considered.
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