Spectral properties of Faddeev's equations

Research outputpeer-review

7 Citations (Scopus)

Abstract

The spectral properties of the matrix operators corresponding to the three-particle Faddeev equations are investigated. It is shown that these operators have two types of invariant subspace. On the subspaces of the first type, the operators possess an eigenvalue spectrum identical to the spectrum of the three-particle Hamiltonian, while the eigenfunctions can be expressed in terms of solutions of the Schrödinger equation. On the subspaces of the second type, the operators are equivalent to the kinetic-energy operator of the system, and therefore their eigenfunctions do not correspond to the dynamics of the interacting particles.

Original languageEnglish
Pages (from-to)235-244
Number of pages10
JournalTheoretical and Mathematical Physics
Volume102
Issue number3
DOIs
Publication statusPublished - 1 Mar 1995

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Faddeev equations
Spectral Properties
operators
Operator
Eigenfunctions
Subspace
eigenvectors
Operator Matrix
Invariant Subspace
Kinetic energy
Eigenvalue
eigenvalues
kinetic energy
matrices

Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

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abstract = "The spectral properties of the matrix operators corresponding to the three-particle Faddeev equations are investigated. It is shown that these operators have two types of invariant subspace. On the subspaces of the first type, the operators possess an eigenvalue spectrum identical to the spectrum of the three-particle Hamiltonian, while the eigenfunctions can be expressed in terms of solutions of the Schr{\"o}dinger equation. On the subspaces of the second type, the operators are equivalent to the kinetic-energy operator of the system, and therefore their eigenfunctions do not correspond to the dynamics of the interacting particles.",
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Spectral properties of Faddeev's equations. / Yakovlev, S. L.

In: Theoretical and Mathematical Physics, Vol. 102, No. 3, 01.03.1995, p. 235-244.

Research outputpeer-review

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AB - The spectral properties of the matrix operators corresponding to the three-particle Faddeev equations are investigated. It is shown that these operators have two types of invariant subspace. On the subspaces of the first type, the operators possess an eigenvalue spectrum identical to the spectrum of the three-particle Hamiltonian, while the eigenfunctions can be expressed in terms of solutions of the Schrödinger equation. On the subspaces of the second type, the operators are equivalent to the kinetic-energy operator of the system, and therefore their eigenfunctions do not correspond to the dynamics of the interacting particles.

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