2009/06/06 by Carl M. Bender, Karim Besseghir, H. F. Jones +2
Chemistry · Mathematics · Physics and Astronomy · #Combinatorics #Eigenvalues and eigenvectors #Hamiltonian (control theory) #Hermitian matrix #Isospectral #Mathematical physics #Mathematics #Operator (biology) #Physics #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Quantum mechanics #Synthesis and Properties of Aromatic Compounds #hep-th
paper · pdf · doi:10.1088/1751-8113/42/35/355301
published as J.Phys.A42:355301,2009 · 11 pages, 1 figure
arxiv created 2009/06/06 · openalex publication_date 2009/08/12 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06
The energy eigenvalues of the class of non-Hermitian -symmetric Hamiltonians H = p 2 + x 2 (i x ) ( ⩾ 0) are real, positive and discrete. The behavior of these eigenvalues has been studied perturbatively for small . However, until now no other features of H have been examined perturbatively. In this paper the small- expansion of the operator and the equivalent isospectral Dirac–Hermitian Hamiltonian h are derived.