Weak pseudo-bosons

Abstract

We show how the notion of {\em 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.

References in corpus (4)

• Non-Hermitian Hamiltonian for a Modulated Jaynes-Cummings Model with PT Symmetry
• A no-go result for the quantum damped harmonic oscillator
• Vector coherent states and intertwining operators
• Coordinate representation for non Hermitian position and momentum operators

Cited by in corpus (7)

• Abstract ladder operators and their applications
• Topological decompositions of the Pauli group and their influence on dynamical systems
• Susy for non-Hermitian Hamiltonians, with a view to coherent states
• Bi-coherent states as generalized eigenstates of the position and the momentum operators
• Quantization of nonlinear non-Hamiltonian systems
• Multiplication of distributions in a linear gain and loss system
• A Swanson-like Hamiltonian and the inverted harmonic oscillator