A new class of non-Hermitian Hamiltonians with real spectra

Abstract

We construct a new class of non-Hermitian Hamiltonians with real spectra. The Hamiltonians possess one explicitly known eigenfunction.

6 pages

References in corpus (5)

• Pseudo-Hermiticity versus PT Symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian
• Pseudo-Hermiticity versus PT-Symmetry II: A complete characterizatio n of non-Hermitian Hamiltonians with a real spectrum
• Spectral equivalences, Bethe Ansatz equations, and reality properties in PT-symmetric quantum mechanics
• Generalized Continuity Equation and Modified Normalization in PT-Symmetric Quantum Mechanics
• Factorization and superpotential of the PT symmetric Hamiltonian

Cited by in corpus (17)

• Quasi-Hermiticity in infinite-dimensional Hilbert spaces
• Two-dimensional SUSY-pseudo-Hermiticity without separation of variables
• PT/Non-PT Symmetric and Non-Hermitian Poschl-Teller-Like Solvable Potentials via Nikiforov-Uvarov Method
• $\eta$-weak-Pseudo-Hermiticity generators and exact solvability
• Non-Hermitian d-dimensional Hamiltonians with position dependent mass and their $\eta$-pseudo-Hermiticity generators
• C, PT, and CPT invariance of pseudo-Hermitian Hamiltonians
• Non-Hermitian von Roos Hamiltonian's $\eta$-weak-pseudo-Hermiticity, isospectrality and exact solvability
• First-order intertwining operators with position dependent mass and $\eta$- weak-psuedo-Hermiticity generators
• Complex Berry phase and imperfect non-Hermitian phase transitions
• Pseudo-reality and pseudo-adjointness of Hamiltonians
• Equivalent Hermitian operator from supersymmetric quantum mechanics
• $\eta$-weak-pseudo-Hermiticity generators and radially symmetric Hamiltonians
• Spherical-separablility of non-Hermitian Hamiltonians and pseudo-PT-symmetry
• Spherical-separablility of non-Hermitian Dirac Hamiltonians and pseudo-PT-symmetry
• Supersymmetric $\eta$ operators
• An update on coherent scattering from complex non-PT-symmetric Scarf II potential with new analytic forms
• Hilbert space representation for quasi-Hermitian position-deformed Heisenberg algebra and Path integral formulation