On the metric operator for the imaginary cubic oscillator

D. Krejčiřík, Petr Siegl

Publikation: Beitrag in einer FachzeitschriftArtikelBegutachtung


We show that the eigenvectors of the PT-symmetric imaginary cubic oscillator are complete, but do not form a Riesz basis. This results in the existence of a bounded metric operator having intrinsic singularity reflected in the inevitable unboundedness of the inverse. Moreover, the existence of nontrivial pseudospectrum is observed. In other words, there is no quantum-mechanical Hamiltonian associated with it via bounded and boundedly invertible similarity transformations. These results open new directions in physical interpretation of PT-symmetric models with intrinsically singular metric, since their properties are essentially different with respect to self-adjoint Hamiltonians, for instance, due to spectral instabilities.

FachzeitschriftPhysical Review D - Particles, Fields, Gravitation and Cosmology
PublikationsstatusVeröffentlicht - 4 Dez. 2012
Extern publiziertJa

ASJC Scopus subject areas

  • Kern- und Hochenergiephysik
  • Physik und Astronomie (sonstige)


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