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SUSY Quantum Mechanics with Complex Superpotentials and Real Energy Spectra | | A.A. Andrianov
; F. Cannata
; J.-P. Dedonder
; M.V. Ioffe
; | | Date: |
5 Jun 1998 | | Journal: | Int.J.Mod.Phys. A14 (1999) 2675-2688 | | Subject: | Quantum Physics; Exactly Solvable and Integrable Systems | quant-ph hep-th nlin.SI solv-int | | Affiliation: | St. Petersburg State University, Dipartimento di Fisica and INFN, Bologna, Université Paris7 - Denis Diderot and Division de Physique Théorique, IPN, Orsay | | Abstract: | We extend the standard intertwining relations used in Supersymmetrical (SUSY) Quantum Mechanics which involve real superpotentials to complex superpotentials. This allows to deal with a large class of non-hermitean Hamiltonians and to study in general the isospectrality between complex potentials. In very specific cases we can construct in a natural way "quasi-complex" potentials which we define as complex potentials having a global property such as to lead to a Hamiltonian with real spectrum. We also obtained a class of complex transparent potentials whose Hamiltonian can be intertwined to a free Hamiltonian. We provide a variety of examples both for the radial problem (half axis) and for the standard one-dimensional problem (the whole axis), including remarks concerning scattering problems. | | Source: | arXiv, quant-ph/9806019 | | Services: | Forum | Review | PDF | Favorites | |
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