Non linear pseudo-bosons

Abstract

In a series of recent papers the author has introduced the notion of (regular) pseudo-bosons showing, in particular, that two number-like operators, whose spectra are ${\mathbb{N}}_0:=\mathbb{N}\cup \{0\}$, can be naturally introduced. Here we extend this construction to operators with rather more general spectra. Of course, this generalization can be applied to many more physical systems. We discuss several examples of our framework.

In press in Journal of Mathematical Physics

References in corpus (1)

• New nonlinear coherent states associated to inverse bosonic and $f$-deformed ladder operators

Cited by in corpus (12)

• Linear Pseudo-fermions
• More mathematics for pseudo-bosons
• Quantizations from reproducing kernel spaces
• Non linear pseudo-bosons versus hidden Hermiticity. II: The case of unbounded operators
• Intertwining operators for non self-adjoint Hamiltonians and bicoherent states
• Non linear pseudo-bosons versus hidden Hermiticity
• Generalized Heisenberg algebra and (non linear) pseudo-bosons
• Bi-squeezed states arising from pseudo-bosons
• Appearances of pseudo-bosons from Black-Scholes equation
• Damping and Pseudo-fermions
• Weak commutation relations of unbounded operators: nonlinear extensions
• Pseudo-bosons for the $D_2$ type quantum Calogero model