Construction of pseudo-bosons systems

Abstract

In a recent paper we have considered an explicit model of a PT-symmetric system based on a modification of the canonical commutation relation. We have introduced the so-called {\em pseudo-bosons}, and the role of Riesz bases in this context has been analyzed in detail. In this paper we consider a general construction of pseudo-bosons based on an explicit {coordinate-representation}, extending what is usually done in ordinary supersymmetric quantum mechanics. We also discuss an example arising from a linear modification of standard creation and annihilation operators, and we analyze its connection with coherent states.

In press in Journal of Mathematical Physics

References in corpus (4)

• PT-symmetric quantum mechanics
• Pseudo-bosons, Riesz bases and coherent states
• Intertwining operators between different Hilbert spaces: connection with frames
• Vector coherent states and intertwining operators

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• Non linear pseudo-bosons versus hidden Hermiticity
• $\mathcal{D}$ pseudo-bosons in quantum models
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• On the presence of families of pseudo-bosons in nilpotent Lie algebras of arbitrary corank
• Pseudo-Bosons from Landau Levels
• Nonlinear n-Pseudo Fermions
• Modified Landau levels, damped harmonic oscillator and two-dimensional pseudo-bosons
• Fermionic model with a non-Hermitian Hamiltonian
• Spectral analysis of a selected non self-adjoint Hamiltonian in an infinite dimensional Hilbert space
• Pseudo-bosons and bi-coherent states out of $\Lc^2(\mathbb{R})$