Weak pseudo-bosons
arXiv:2001.05219 · doi:10.1088/1751-8121/ab766f
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.
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- 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