•  
  •  
 

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

Abstract

We consider a family of discrete Schrödinger operators $H(K),\,K\in (-\pi,\pi]^5$ associated with a system of three quantum particles on the five-dimensional lattice ${\mathbb{Z}}^5$ interacting via short-range pair potentials and having arbitrary "dispersion functions" with not necessarily compact support.

We show that the essential spectrum of the three-particle discrete Schr\"odinger operator $H(K),\,K\in (-\pi,\pi]^5$ consists of a finitely many bounded closed intervals.

First Page

152

Last Page

168

References

1. S.Albeverio, S.N. Lakaev, Z.I. Muminov, Schrodinger operators on lattices. The Efimov effect and discrete spectrum asymptotics, Ann. Inst. H. Poincar Phys. Theor. 5 (2004) 1-30.

2. Albeverio, S., Lakaev, S., Muminov, Z.: On the structure of the essential spectrum for the three-particle Schrodinger operators on lattices. Math. Nachr. 280, 699--716 (2007).

3. V.Enss, A Note on Hunziker's Theorem, Comm. Math. Phys. 52 (1977), 233-238.

4. L.D. Faddeev, Mathematical aspects of the three--body problem in quantum mechanics, Israel Program for Scientific Translations, Jerusalem, 1965.

5. L.D.Faddeev and S.P.Merkuriev, Quantum scattering theory for several particle systems, Kluwer Academic Publishers, 1993.

Share

COinS
 
 

To view the content in your browser, please download Adobe Reader or, alternately,
you may Download the file to your hard drive.

NOTE: The latest versions of Adobe Reader do not support viewing PDF files within Firefox on Mac OS and if you are using a modern (Intel) Mac, there is no official plugin for viewing PDF files within the browser window.