33 citations · 60 across the 14 of their papers we have counts for
15 papers
An unified approach for the (inverted) quantum harmonic oscillator and the Berry-Keating hamiltonian
Fabio Bagarello, Emanuele Balistreri, Sergey Kuzhel
We propose an unified view to three well known quadratic Hamiltonians widely considered in quantum mechanics, i.e. those of the harmonic oscillator, of the inverted harmonic oscill…
On the Berry-Keating Operator
Fabio Bagarello, Sergiusz Kużel
We review here two different viewpoints on the Berry-Keating operator , whose connection to the Riemann hypothesis remains an intriguing and not yet fully understood questi…
A position dependent mass Hamiltonian and abstract ladder operators
Fabio Bagarello, Emanuele Balistreri, Antonino Faddetta
We consider the Hamiltonian of a particle in one dimension with a position dependent mass for which we apply the recent strategy of the so-called {\em abstract ladder operators…
New results for Heisenberg dynamics for non self-adjoint Hamiltonians
Fabio Bagarello
In a previous paper we began our analysis on the role of non self-adjoint Hamiltonians in connection with the Heisenberg dynamics for quantum systems. Here, motivated by the growin…
A pseudo-bosonic Klein-Gordon field with finite two-points function
Fabio Bagarello
We introduce a class of pseudo-bosonic Klein-Gordon fields in 1+1 dimensions and we discuss some of their properties. This work originates from non Hermitian quantum mechanics and…
Some Consequences of the Grunewald-O'Halloran Conjecture for Pseudoquonic Operators
Fabio Bagarello, Yanga Bavuma, Francesco G. Russo
Investigating a recent positive solution of a conjecture of Grunewald and O'Halloran for complex finite dimensional nilpotent Lie algebras, we are in the position to find results o…
Eigenstates of CQ*-algebras
Fabio Bagarello, Hiroshi Inoue, Camillo Trapani +1
Motivated by some recent results, we consider the notion of eigenstate (and eigenvalue) for an element of a CQ*-algebras and the consequences on algebraic quantum dynamics and…
-product of distributions, with applications
Fabio Bagarello
We consider and reformulate a recent definition of multiplication between distributions. We show that this definition can be adopted, in particular, to prove biorthonormality of so…
Sesquilinear forms as eigenvectors in quasi *-algebras, with an application to ladder elements
Fabio Bagarello, Hiroshi Inoue, Salvatore Triolo
We consider a particular class of sesquilinear forms on a {Banach quasi *-algebra} $(\A[\|.\|],\Ao[\|.\|_0])$ which we call {\em eigenstates of an element} $a\in\A$, and we deduce…
On Positive Vectors in Indefinite Inner Product Spaces
Fabio Bagarello, Sergiusz Kuzel
Let be a linear space equipped with an indefinite inner product . Denote by the nonlinear set of…
A new family of ladder operators for macroscopic systems, with applications
Fabio Bagarello
In a series of recent scientific contributions the role of bosonic and fermionic ladder operators in a macroscopic realm has been investigated. Creation, annihilation and number op…
Unbounded Hamiltonians generated by Parseval frames
Fabio Bagarello, Sergiusz Kużel
In \cite{BK} Parseval frames were used to define bounded Hamiltonians, both in finite and in infinite dimesional Hilbert spaces. Here we continue this analysis, with a particular f…
Heisenberg dynamics for non self-adjoint Hamiltonians: symmetries and derivations
Fabio Bagarello
In some recent literature the role of non self-adjoint Hamiltonians, , is often considered in connection with gain-loss systems. The dynamics for these systems is,…
Non-self-adjoint hamiltonians defined by Riesz bases
F. Bagarello, A. Inoue, C. Trapani
We discuss some features of non-self-adjoint Hamiltonians with real discrete simple spectrum under the assumption that the eigenvectors form a Riesz basis of Hilbert space. Among o…
Mathematical aspects of intertwining operators: the role of Riesz bases
Fabio Bagarello
In this paper we continue our analysis of intertwining relations for both self-adjoint and not self-adjoint operators. In particular, in this last situation, we discuss the connect…