# Nonlinear pseudo-bosons

@article{Bagarello2011NonlinearP, title={Nonlinear pseudo-bosons}, author={Fabio Bagarello}, journal={Journal of Mathematical Physics}, year={2011}, volume={52}, pages={063521-063521} }

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 N0:=N∪{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.

## 16 Citations

### Linear pseudo-fermions

- Physics
- 2012

This article repeats a similar analysis starting with the canonical anticommutation relations, and shows that in this case, most of the assumptions needed in the former situation are automatically satisfied, making the construction rather friendly.

### Generalized Heisenberg algebra and (non linear) pseudo-bosons

- Physics, Mathematics
- 2018

We propose a deformed version of the generalized Heisenberg algebra by using techniques borrowed from the theory of pseudo-bosons. In particular, this analysis is relevant when non self-adjoint…

### More mathematics for pseudo-bosons

- Mathematics
- 2013

We propose an alternative definition for pseudo-bosons. This simplifies the mathematical structure, minimizing the required assumptions. Some physical examples are discussed, as well as some…

### Nonlinear pseudo-bosons versus hidden Hermiticity: II. The case of unbounded operators

- Physics
- 2012

A close parallelism between the notions of nonlinear pseudobosons and those of an apparent non-Hermiticity of observables as shown in part I (2011 J. Phys. A: Math. Theor. 44 415305) is demonstrated…

### Damping and pseudo-fermions

- Physics
- 2012

After a short abstract introduction on the time evolution driven by non-self-adjoint Hamiltonians, we show how the recently introduced concept of pseudo-fermion can be used in the description of…

### Intertwining operators for non-self-adjoint Hamiltonians and bicoherent states

- Physics, Mathematics
- 2016

This paper is devoted to the construction of what we will call exactly solvable models, i.e., of quantum mechanical systems described by an Hamiltonian H whose eigenvalues and eigenvectors can be…

### Se p 20 18 Bi-squeezed states arising from pseudo-bosons

- Physics
- 2018

Extending our previous analysis on bi-coherent states, we introduce here a new class of quantum mechanical vectors, the bi-squeezed states, and we deduce their main mathematical properties. We relate…

### Appearances of pseudo-bosons from Black-Scholes equation

- Physics
- 2016

It is a well known fact that the Black-Scholes equation admits an alternative representation as a Schrodinger equation expressed in terms of a non-self-adjoint Hamiltonian. We show how pseudo-bosons,…

### Weak commutation relations of unbounded operators: Nonlinear extensions

- Mathematics
- 2012

We continue our analysis of the consequences of the commutation relation [S,T]=1, where S and T are two closable unbounded operators. The weak sense of this commutator is given in terms of the inner…

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