2001/02/19 by B. Bagchi, B. BAGCHI, S. Mallik +3 · 6 citations
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics #hep-th #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1142/s0217751x01004153
published as Int.J.Mod.Phys. A16 (2001) 2859-2872 · 20 pages, Latex 2e + amssym + graphics, 2 figures, accepted in Int. J. Mod. Phys. A
arxiv created 2001/02/19 · openalex publication_date 2001/06/30 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
In the framework of SUSYQM extended to deal with non-Hermitian Hamiltonians, we analyze three sets of complex potentials with real spectra, recently derived by a potential algebraic approach based upon the complex Lie algebra [Formula: see text] . This extends to the complex domain the well-known relationship between SUSYQM and potential algebras for Hermitian Hamiltonians, resulting from their common link with the factorization method and Darboux transformations. In the same framework, we also generate for the first time a pair of elliptic partner potentials of Weierstrass ℘ type, one of them being real and the other imaginary and PT symmetric. The latter turns out to be quasiexactly solvable with one known eigenvalue corresponding to a bound state. When the Weierstrass function degenerates to a hyperbolic one, the imaginary potential becomes PT nonsymmetric and its known eigenvalue corresponds to an unbound state.