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2005-05-22 - Article/Dans un journal avec peer-review - Anglais - 14 page(s)

Fairlie D.B., Nuyts Jean , "Fock space representations for non-Hermitian Hamiltonians" in Journal of Physics : A Mathematical & General, 38, 16, 3611-3624

  • Edition : Institute of Physics, Bristol (United Kingdom)
  • Codes CREF : Physique des particules élémentaires (DI1221), Physique théorique et mathématique (DI1210)
  • Unités de recherche UMONS : Physique théorique et mathématique (S814)
Texte intégral :

Abstract(s) :

(Anglais) The requirement of Hermiticity of a quantum mechanical Hamiltonian, for the description of physical processes with real eigenvalues which has been challenged notably by Carl Bender, is examined for the case of a Fock space Hamiltonian which is bilinear in two creation and annihilation operators. An interpretation of this model as a Schrödinger operator leads to an identification of the Hermitian form of the Hamiltonian as the Landau model of a charged particle in a plane, interacting with a constant magnetic field at right angles to the plane. When the parameters of the Hamiltonian are suitably adjusted to make it non-Hermitian, the model represents two harmonic oscillators at right angles interacting with a constant magnetic field in the third direction, but with a pure imaginary coupling, and real energy eigenvalues. It is now PT symmetric. Multiparticle states are investigated.

Identifiants :
  • DOI : 10.1088/0305-4470/38/16/010
  • EPRINT : hep-th/0412148
  • ISSN : 0305-4470