2006/09/03 by A. D. Alhaidari, A D Alhaidari · 4 citations
Mathematics · Physics and Astronomy · #Algebra over a field #Algebraic structures and combinatorial models #Differential operator #Extension (predicate logic) #Hamiltonian (control theory) #Lie superalgebra #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics #Realization (probability) #Superalgebra #Symmetry (geometry) #Wave function #physics.atom-ph #physics.optics
paper · pdf · doi:10.1088/0305-4470/39/50/007
published in Journal of Physics A Mathematical and General 39(50), 15391-15401 (Institute of Physics) · 12 pages, no figures
arxiv created 2006/09/03 · openalex publication_date 2006/11/30 · arxiv updated 2009/12/01 · openalex created_date 2019/06/27 · openalex updated_date 2026/08/05
The super-algebraic structure of a generalized version of the Jaynes–Cummings model is investigated. We find that a Z 2 graded extension of the so (2,1) Lie algebra is the underlying symmetry of this model. It is isomorphic to the four-dimensional super-algebra u (1/1) with two odd and two even elements. Differential matrix operators are taken as realization of the elements of the superalgebra to which the model Hamiltonian belongs. Several examples with various choices of superpotentials are presented. The energy spectrum and corresponding wavefunctions are obtained analytically.