Hermitian Hamiltonian equivalent to a given non-Hermitian one: manifestation of spectral singularity.
نویسنده
چکیده
One of the simplest non-Hermitian Hamiltonians, first proposed by Schwartz in 1960, that may possess a spectral singularity is analysed from the point of view of the non-Hermitian generalization of quantum mechanics. It is shown that the η operator, being a second-order differential operator, has supersymmetric structure. Asymptotic behaviour of the eigenfunctions of a Hermitian Hamiltonian equivalent to the given non-Hermitian one is found. As a result, the corresponding scattering matrix and cross section are given explicitly. It is demonstrated that the possible presence of a spectral singularity in the spectrum of the non-Hermitian Hamiltonian may be detected as a resonance in the scattering cross section of its Hermitian counterpart. Nevertheless, just at the singular point, the equivalent Hermitian Hamiltonian becomes undetermined.
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ورودعنوان ژورنال:
- Philosophical transactions. Series A, Mathematical, physical, and engineering sciences
دوره 371 1989 شماره
صفحات -
تاریخ انتشار 2013