Transition probabilities for non self-adjoint Hamiltonians in infinite dimensional Hilbert spaces

Fabio Bagarello, Bagarello

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

In a recent paper we have introduced several possible inequivalent descriptions of the dynamics and of the transition probabilities of a quantum system when its Hamiltonian is not self-adjoint. Our analysis was carried out in finite dimensional Hilbert spaces. This is useful, but quite restrictive since many physically relevant quantum systems live in infinite dimensional Hilbert spaces. In this paper we consider this situation, and we discuss some applications to well known models, introduced in the literature in recent years: the extended harmonic oscillator, the Swanson model and a generalized version of the Landau levels Hamiltonian. Not surprisingly we will find new interesting features not previously found in finite dimensional Hilbert spaces, useful for a deeper comprehension of this kind of physical systems.
Original languageEnglish
Pages (from-to)424-435
Number of pages12
JournalAnnals of Physics
Volume362
Publication statusPublished - 2015

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Hilbert space
transition probabilities
harmonic oscillators

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

Cite this

Transition probabilities for non self-adjoint Hamiltonians in infinite dimensional Hilbert spaces. / Bagarello, Fabio; Bagarello.

In: Annals of Physics, Vol. 362, 2015, p. 424-435.

Research output: Contribution to journalArticle

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