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JOURNALS // Teoreticheskaya i Matematicheskaya Fizika // Archive

TMF, 2000 Volume 123, Number 1, Pages 81–87 (Mi tmf587)

This article is cited in 2 papers

Essential Schrödinger operator spectrum of one system of four particles on a lattice

Zh. I. Abdullaev

A. Navoi Samarkand State University

Abstract: The energy operator of a system of four particles on a lattice where only two pairs of the particles interact is considered. There exist four mutually orthogonal subspaces, invariant with respect to the energy operator and such that their direct sum is equal to the entire space. The spectra of the restrictions of the energy operator to these invariant spaces are found. The dependence of the essential spectrum on the binary interaction is examined. The absence of bound states of this operator is demonstrated.

Received: 01.07.1999

DOI: 10.4213/tmf587


 English version:
Theoretical and Mathematical Physics, 2000, 123:1, 483–488

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