2008/06/27 by A. Sinha, Anjana Sinha, P. Roy +1
Mathematics · Physics and Astronomy · #Creation and annihilation operators #Formalism (music) #Ground state #Hamiltonian (control theory) #Hermitian matrix #Invariant (physics) #Isospectral #Mathematical physics #Mathematics #Matrix similarity #Nonlinear Waves and Solitons #Partial differential equation #Physics #Pure mathematics #Quantum #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Quantum mechanics #Supersymmetry #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1088/1751-8113/41/33/335306
22 pages, to be published in J. Phys. A
arxiv created 2008/06/27 · openalex publication_date 2008/07/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
New non Hermitian Hamiltonians are generated, as isospectral partners of the generalized Swanson model, viz., , where α, β are real constants, with α ≠ β, and and are generalized creation and annihilation operators. It is shown that the initial Hamiltonian H − , and its partner H + , are related by pseudo supersymmetry, and they share all the eigen energies except for the ground state. This pseudo supersymmetric extension enlarges the class of non Hermitian Hamiltonians H ± , related to their respective Hermitian counterparts h ± , through the same similarity transformation operator ρ: H ± = ρ −1 h ± ρ. The formalism is applied to the entire class of shape-invariant models.