On unitarity of the scattering operator in non-Hermitian quantum mechanics - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2023

On unitarity of the scattering operator in non-Hermitian quantum mechanics

Résumé

We consider the Schrödinger operator with regular short range complex-valued potential in dimension d ≥ 1. We show that, for d ≥ 2, the unitarity of scattering operator for this Hamiltonian at high energies implies the reality of potential (that is Hermiticity of Hamiltonian). In contrast, for d = 1, we present complex-valued exponentially localized soliton potentials with unitary scattering operator for all positive energies and with unbroken PT symmetry. We also present examples of complex-valued regular short range potentials with real spectrum for d = 3. Some directions for further research are formulated.
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Dates et versions

hal-03989986 , version 1 (15-02-2023)

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  • HAL Id : hal-03989986 , version 1

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Roman Novikov, Iskander Taimanov. On unitarity of the scattering operator in non-Hermitian quantum mechanics. 2023. ⟨hal-03989986⟩
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