التفاصيل البيبلوغرافية
| العنوان: |
On Unitarity of the Scattering Operator in Non-Hermitian Quantum Mechanics. |
| المؤلفون: |
Novikov, R. G., Taimanov, I. A. |
| المصدر: |
Annales Henri Poincaré; Aug2024, Vol. 25 Issue 8, p3899-3909, 11p |
| مصطلحات موضوعية: |
QUANTUM mechanics, QUANTUM operators, HAMILTONIAN operator, POSITIVE operators, SCHRODINGER operator, HERMITIAN operators, SCATTERING (Mathematics), INVERSE scattering transform |
| مستخلص: |
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 the 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. [ABSTRACT FROM AUTHOR] |
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| قاعدة البيانات: |
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