Metric operators, generalized hermiticity and lattices of Hilbert spaces

Camillo Trapani, Jean-Pierre Antoine

Risultato della ricerca: Chapter

14 Citazioni (Scopus)

Abstract

Pseudo-Hermitian quantum mechanics (QM) is a recent, unconventional, approach to QM, based on the use of non-self-adjoint Hamiltonians, whose self-adjointness can be restored by changing the ambient Hilbert space, via a so-called metric operator. The PT-symmetric Hamiltonians are usually pseudo-Hermitian operators, a term introduced a long time ago by Dieudonné for characterizing those bounded operators A that satisfy a relation of the form GA = A G, where G is a metric operator, that is, a strictly positive self-adjoint operator. This chapter explores further the structure of unbounded metric operators, in particular, their incidence on similarity. It examines the notion of similarity between operators induced by a bounded metric operator with bounded inverse. The goal here is to study which spectral properties are preserved under such a quasi-similarity relation. The chapter applies some of the previous results to operators on the scale of Hilbert spaces generated by the metric operator.
Lingua originaleEnglish
Titolo della pubblicazione ospiteNon-Self-adjoint Operators in Quantum Physics
Pagine345-402
Numero di pagine58
Stato di pubblicazionePublished - 2015

All Science Journal Classification (ASJC) codes

  • ???subjectarea.asjc.3100.3100???
  • ???subjectarea.asjc.2200.2200???
  • ???subjectarea.asjc.2600.2600???

Fingerprint Entra nei temi di ricerca di 'Metric operators, generalized hermiticity and lattices of Hilbert spaces'. Insieme formano una fingerprint unica.

Cita questo