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# The Faddeev equation and essential spectrum of a Hamiltonian in Fock space

### Abstract

A Hamiltonian (model operator) $H$ associated to a quantum system describing three particles in interaction, without conservation of the number of particles, is considered. The Faddeev type system of equations for eigenvectors of $H$ is constructed. The essential spectrum of $H$ is described by the spectrum of the channel operator.

### Article Information

 Title The Faddeev equation and essential spectrum of a Hamiltonian in Fock space Source Methods Funct. Anal. Topology, Vol. 17 (2011), no. 1, 47-57 MathSciNet MR2815372 Copyright The Author(s) 2011 (CC BY-SA)

### Authors Information

Mukhiddin I. Muminov
Samarkand State University, Department of Physics and Mathematics, 15 University Boulevard, Samarkand, 140104, Uzbekistan

Tulkin H. Rasulov
Bukhara State University, Faculty of Physics and Mathematics, Department of Algebra and Analysis, 11 M. Ikbol, Bukhara, 200100, Uzbekistan

### Citation Example

Mukhiddin I. Muminov and Tulkin H. Rasulov, The Faddeev equation and essential spectrum of a Hamiltonian in Fock space, Methods Funct. Anal. Topology 17 (2011), no. 1, 47-57.

### BibTex

@article {MFAT550,
AUTHOR = {Muminov, Mukhiddin I. and Rasulov, Tulkin H.},
TITLE = {The Faddeev equation and essential spectrum of a Hamiltonian in Fock space},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {17},
YEAR = {2011},
NUMBER = {1},
PAGES = {47-57},
ISSN = {1029-3531},
URL = {http://mfat.imath.kiev.ua/article/?id=550},
}