Finite-dimensional pseudo-bosons: A non-Hermitian version of the truncated harmonic oscillator

Fabio Bagarello, Bagarello

Research output: Contribution to journalArticle

Abstract

We propose a deformed version of the commutation rule introduced in 1967 by Buchdahl to describe a particular model of the truncated harmonic oscillator. The rule we consider is defined on a N-dimensional Hilbert space H N , and produces two biorthogonal bases of H N which are eigenstates of the Hamiltonians h=[Formula presented](q 2 +p 2 ), and of its adjoint h † . Here q and p are non-Hermitian operators obeying [q,p]=i(1−Nk), where k is a suitable orthogonal projection operator. These eigenstates are connected by ladder operators constructed out of q, p, q † and p † . Some examples are discussed.
Original languageEnglish
Pages (from-to)2526-2532
Number of pages7
JournalPHYSICS LETTERS A
Volume382
Publication statusPublished - 2018

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harmonic oscillators
bosons
operators
eigenvectors
commutation
Hilbert space
ladders
projection

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

Cite this

Finite-dimensional pseudo-bosons: A non-Hermitian version of the truncated harmonic oscillator. / Bagarello, Fabio; Bagarello.

In: PHYSICS LETTERS A, Vol. 382, 2018, p. 2526-2532.

Research output: Contribution to journalArticle

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