Pseudo-Supersymmetric Quantum Mechanics and Isospectral Pseudo-Hermi tian Hamiltonians

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dc.creatorMostafazadeh, Ali
dc.date2002-03-21
dc.date2002-05-07
dc.date.accessioned2026-07-07T11:10:37Z
dc.date.available2026-07-07T11:10:37Z
dc.descriptionWe examine the properties and consequences of pseudo-supersymmetry for quantum systems admitting a pseudo-Hermitian Hamiltonian. We explore the Witten index of pseudo-supersymmetry and show that every pair of diagonalizable (not necessarily Hermitian) Hamiltonians with discrete spectra and real or complex-conjugate pairs of eigenvalues are isospectral and have identical degeneracy structure except perhaps for the zero eigenvalue if and only if they are pseudo-supersymmetric partners. This implies that pseudo-supersymmetry is the basic framework for generating non-Hermitian PT-symmetric and non-PT-symmetric Hamiltonians with a real spectrum via a Darboux transformation, and shows that every diagonalizable Hamiltonian H with a discrete spectrum and real or complex-conjugate pairs of eigenvalues may be factored as H=L^# L where L is a linear operator with pseudo-adjoint L^#. In particular, this factorization applies to PT-symmetric and Hermitian Hamiltonians. The nondegenerate two-level systems provide a class of Hamiltonians that are pseudo-Hermitian. We demonstrate the implications of our general results for this class in some detail.
dc.descriptionMinor corrections, accepted for publication in Nucl. Phys. B
dc.identifierhttps://arxiv.org/abs/math-ph/0203041
dc.identifierhttp://arxiv.org/abs/math-ph/0203041
dc.identifierNucl.Phys.B640:419-434,2002
dc.identifierdoi:10.1016/S0550-3213(02)00347-4
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/190829
dc.subjectMathematical Physics
dc.subjectHigh Energy Physics - Theory
dc.subjectQuantum Physics
dc.titlePseudo-Supersymmetric Quantum Mechanics and Isospectral Pseudo-Hermi tian Hamiltonians
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