### 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 language | English |
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Pages (from-to) | 235-244 |

Number of pages | 10 |

Journal | Theoretical and Mathematical Physics |

Volume | 102 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1 Mar 1995 |

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### Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

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*Theoretical and Mathematical Physics*, vol. 102, no. 3, pp. 235-244. https://doi.org/10.1007/BF01017873

**Spectral properties of Faddeev's equations.** / Yakovlev, S. L.

Research output › › peer-review

TY - JOUR

T1 - Spectral properties of Faddeev's equations

AU - Yakovlev, S. L.

PY - 1995/3/1

Y1 - 1995/3/1

N2 - 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.

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.

UR - http://www.scopus.com/inward/record.url?scp=0002372877&partnerID=8YFLogxK

U2 - 10.1007/BF01017873

DO - 10.1007/BF01017873

M3 - Article

VL - 102

SP - 235

EP - 244

JO - Theoretical and Mathematical Physics

JF - Theoretical and Mathematical Physics

SN - 0040-5779

IS - 3

ER -