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On the essential spectrum of a four-particle Schrödinger operator on a lattice

Abstract

The Hamiltonian of a system of four arbitrary quantum particles with three-particle short-range interaction potentials on a three-dimensional lattice is examined. The location of the essential spectrum of this Hamiltonian is described by Faddeev’s equations.

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Correspondence to M. I. Muminov.

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Original Russian Text © M. I. Muminov and U. R. Shodiev, 2010, published in Matematicheskie Trudy, 2010, Vol. 13, No. 1, pp. 169–185.

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Muminov, M.I., Shodiev, U.R. On the essential spectrum of a four-particle Schrödinger operator on a lattice. Sib. Adv. Math. 21, 292–303 (2011). https://doi.org/10.3103/S1055134411040079

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Keywords

  • Schrödinger operator
  • Faddeev’s equations
  • essential spectrum
  • compact operator
  • positive operator