Physics – Mathematical Physics
Scientific paper
2002-03-21
Nucl.Phys.B640:419-434,2002
Physics
Mathematical Physics
Minor corrections, accepted for publication in Nucl. Phys. B
Scientific paper
10.1016/S0550-3213(02)00347-4
We 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.
No associations
LandOfFree
Pseudo-Supersymmetric Quantum Mechanics and Isospectral Pseudo-Hermi tian Hamiltonians does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Pseudo-Supersymmetric Quantum Mechanics and Isospectral Pseudo-Hermi tian Hamiltonians, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Pseudo-Supersymmetric Quantum Mechanics and Isospectral Pseudo-Hermi tian Hamiltonians will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-665259