# 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…

## 15 Citations

### Structure of T - and S - Matrices in Unphysical Sheets and Resonances in Three - Body Systems

- Physics
- 1998

Algorithm, based on explicit representations for the analytic continuation of Faddeev components of the three-body T-matrix in unphysical energy sheets, is employed to study mechanism of…

### Eigenvectors of the multichannel scattering matrix at resonance energy values

- Physics
- 2014

Explicit representations for the T matrix and the scattering matrix analytically continued to unphysical energy sheets in a multichannel problem featuring binary channels are discussed. From these…

### Unphysical Energy Sheets and Resonances in the Friedrichs–Faddeev Model

- MathematicsFew-Body Systems
- 2019

We consider the Friedrichs–Faddeev model in the case where the kernel of the potential operator is holomorphic in both arguments on a certain domain of $$\mathbb {C}$$C. For this model we, first,…

### Operator Interpretation of Resonances Arising in Spectral Problems for 2 x 2 Matrix Hamiltonians

- Mathematics
- 1998

We consider the analytic continuation of the transfer function for a 2 x 2 matrix Hamiltonian into the unphysical sheets of the energy Riemann surface. We construct non-selfadjoint operators…

### Operator interpretation of the resonances generated by 2×2 matrix Hamiltonians

- Physics
- 1998

An analytic continuation of the transfer function for a 2×2 matrix Hamiltonian to unphysical sheets of the Riemann energy surface is considered. Nonselfadjoint operators are constructed such that…

### Operator interpretation of resonances generated by some operator matrices

- Mathematics
- 2000

We consider the analytic continuation of the transfer function for a 2 × 2 operator matrix into the unphysical sheets of the energy Riemann surface. We construct a family of non-selfadjoint operators…

### 0 Ju n 19 99 OPERATOR INTERPRETATION OF RESONANCES ARISING IN SPECTRAL PROBLEMS FOR 2 × 2 MATRIX HAMILTONIANS ∗ †

- Mathematics
- 2008

We consider the analytic continuation of the transfer function for a 2 × 2 matrix Hamiltonian into the unphysical sheets of the energy Riemann surface. We construct non-selfadjoint operators…

### Unphysical Energy Sheets and Resonances in the Friedrichs–Faddeev Model

- MathematicsFew-Body Systems
- 2019

We consider the Friedrichs–Faddeev model in the case where the kernel of the potential operator is holomorphic in both arguments on a certain domain of C\documentclass[12pt]{minimal}…

### Ultracold collisions in the system of three helium atoms

- Physics
- 2009

The Faddeev differential equations for a system of three particles with a hard-core interaction are described. Numerical results on the binding energies of the 4He3 and 3He4He2 trimers and on…

### Perturbation of a lattice spectral band by a nearby resonance

- Physics
- 2001

A soluble model of weakly coupled “molecular” and “nuclear” Hamiltonians is studied in order to exhibit explicitly the mechanism leading to the enhancement of fusion probability in case of a narrow…

## References

SHOWING 1-10 OF 75 REFERENCES

### Integral equations for resonance and virtual states

- Physics
- 1984

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

- Physics
- 1987

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

- Physics
- 1986

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…

### Lectures on the theory of few-body systems

- Physics
- 1990

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

- Physics
- 1990

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

- Mathematics, Physics
- 1985

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

- Physics, Mathematics
- 1981

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.

- Mathematics
- 1967

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

- Mathematics, Physics
- 1971

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…