1999/06/16 by Carl M. Bender, Stefan Boettcher, H. F. Jones +1 · 2 citations
Mathematics · Physics and Astronomy · #Classical limit #Covariant Hamiltonian field theory #Generalization #Geometry #Good quantum number #Hamiltonian (control theory) #Hamiltonian system #Hermitian matrix #Invariant (physics) #Limit (mathematics) #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear Waves and Solitons #Physics #Quantum #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Quantum mechanics #Square (algebra) #Superintegrable Hamiltonian system #cond-mat #hep-th #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1088/0305-4470/32/39/305
published as J.Phys.A32:6771-6781,1999 · 7 pages, Revtex, 2 eps-figures enclosed
arxiv created 1999/06/16 · openalex publication_date 1999/09/15 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Recently, a class of -invariant quantum mechanical models described by the non-Hermitian Hamiltonian H = p 2 + x 2 (i x ) was studied. It was found that the energy levels for this theory are real for all 0. Here, the limit as is examined. It is shown that in this limit, the theory becomes exactly solvable. A generalization of this Hamiltonian, H = p 2 + x 2 M (i x ) ( M = 1,2,3, ... ) is also studied, and this -symmetric Hamiltonian becomes exactly solvable in the large- limit as well. In effect, what is obtained in each case is a complex analogue of the Hamiltonian for the square-well potential. Expansions about the large- limit are obtained.