Equivalence of the effective Hamiltonian approach and the Siegert boundary condition for resonant states

DOI10.1002/prop.201200064zbMath1338.81256arXiv1405.7021OpenAlexW3106507902MaRDI QIDQ2812929

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Publication date: 13 June 2016

Published in: Fortschritte der Physik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1405.7021

zbMATH Keywords

effective Hamiltoniannon-Hermitian Hamiltonianresonant stateFeshbach formalismSiegert condition

Mathematics Subject Classification ID

Canonical models for contractions and nonselfadjoint linear operators (47A45) Open systems, reduced dynamics, master equations, decoherence (81S22) Nonselfadjoint operator theory in quantum theory including creation and destruction operators (81Q12) Quantum dots, waveguides, ratchets, etc. (81Q37)

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Cites Work

• Unified theory of nuclear reactions
• Spectral properties of many-body Schrödinger operators with dilatation- analytic interactions
• A class of analytic perturbations for one-body Schrödinger Hamiltonians
• Quadratic form techniques and the Balslev-Combes theorem
• A unified theory of nuclear reactions. II
• Causality and dispersion relations in wave mechanics
• The structure of a non-relativistic S -matrix
• Some Properties of the Resonant State in Quantum Mechanics and Its Computation
• A non-Hermitian Hamilton operator and the physics of open quantum systems
• S-matrix theory for transmission through billiards in tight-binding approach
• Nuclear Physics A. Stationary States of Nuclei
• On the Scattering of a Particle by a Static Potential
• Scattering of Ions by Polarization Forces