Representations for the Three‐Body T‐Matrix, Scattering Matrices and Resolvent in Unphysical Energy Sheets

@article{Motovilov1995RepresentationsFT,
  title={Representations for the Three‐Body T‐Matrix, Scattering Matrices and Resolvent in Unphysical Energy Sheets},
  author={Alexander K. Motovilov},
  journal={Mathematische Nachrichten},
  year={1995},
  volume={187}
}
Explicit representations for the Faddeev components of the three‐body T‐matrix continued analytically into unphysical sheets of the energy Riemann surface are formulated. According to the representations, the T‐matrix in unphysical sheets is explicitly expressed in terms of its components taken in the physical sheet only. The representations for the T‐matrix are then used to construct similar representations for the analytic continuation of the three‐body scattering matrices and the resolvent… 

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References

SHOWING 1-10 OF 75 REFERENCES

Integral equations for resonance and virtual states

Integral equations are derived for the resonance and virtual (antibound) states consisting of two or three bodies. The derivation is based on the analytic continuation of the integral equations of

Existence and analyticity of many body scattering amplitudes at low energies

Two‐cluster–two‐cluster scattering amplitudes for N‐body quantum systems are studied. Our attention is restricted to energies below the lowest three‐cluster threshold. For potentials falling off like

N-italic-body quantum problem in configuration space

The scattering problem for systems of N-italic particles is formulated in the configuration representation. The cases of short-range two-body potentials, potentials with Coulomb long-range

Perturbation of resonances in quantum mechanics

Lectures on the theory of few-body systems

1. The Two-Body Problem.- 1.1 Properties of the Two-Particle t-Matrix.- 1.2 Phase-Equivalent Potentials.- 1.3 Separable Expansions of the t-Matrix.- 2. The Fadeev-Equations in the Three-Body Problem.

Extended Hilbert space approach to few-body problems

A general formulation of the quantum scattering theory for a system of few particles, which have an internal structure, is given. Due to freezing out the internal degrees of freedom in the external

Quantum scattering theory for two- and three-body systems with potentials of short and long range

We give a full proof of asymptotic completeness for Schrodinger operators of two- and three-particle quantum systems. The interaction is given by pair potentials which may be of short and of long

Resonance poles and Gamow vectors in the rigged Hilbert space formulation of quantum mechanics

After a summary of the Rigged Hilbert space formulation of quantum mechanics and a brief statement of its advantages over von Neumann’s formulation, a mathematically correct definition of Gamow’s

Scattering Theory for Automorphic Functions.

The application by Fadeev and Pavlov of the Lax-Phillips scattering theory to the automorphic wave equation led Professors Lax and Phillips to reexamine this development within the framework of their

Spectral properties of many-body Schrödinger operators with dilatation-analytic interactions

Quantum mechanicalN-body systems with dilatation analytic interactions are investigated. Absence of continuous singular part for the Hamiltonians is proved together with the existence of an
...