On unitarity of the scattering operator in non-Hermitian quantum mechanics - Archive ouverte HAL
Article Dans Une Revue Annales de l'Institut Henri Poincare Physique Theorique Année : 2024

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)

Identifiants

Citer

Roman Novikov, Iskander Taimanov. On unitarity of the scattering operator in non-Hermitian quantum mechanics. Annales de l'Institut Henri Poincare Physique Theorique, 2024, 25, pp.3899-3909. ⟨10.1007/s00023-024-01414-5⟩. ⟨hal-03989986⟩
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