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Scientific reports of Bukhara State University

Abstract

In the paper a family H(K) , d K ( ; ] of 33 operator matrices associated with the Hamiltonian of a system of three non conserved number of particles on a d -dimensional lattice d Z is considered. Regularized Fredholm determinant whose set of zeros coisides with the discrete spectrum of the operator H(K) is constructed.

First Page

75

Last Page

81

References

1. Jukov Yu.V., Minlos R.A. Spektr i rasseyanie v modeli "spin-bozon" s ne bolee chem tremya fotonami. Teor. i matem. fizika,103 (1995). - № 1. – C. 63-81. Theoret. and Math. Phys., 103:1 (1995), 398-411 faktora, uzb.mat.jurnal. 2012 god № 4. – S. 19-25. 2. Mattis D. The few-body problem on a lattice. Rev. Modern Phys., 58 (1986). - P. 361-379. 3. Fridrixs K.O. Vozmuщenie spektra operatorov v gilbertovom prostranstve. – M.: Mir, 1969. 4. Malыshev V.A., Minlos R.A. Klastepnыe opepatopы. Tpudы seminapa im. I.G. Petpovskogo. (1983), vыp. 9. – C. 63-80. 5. Minlos R.A., Spohn H. The three-body problem in radioactive decay: the case of one atom and at most two photons. Topics in Statistical and Theoretical Physics. Amer. Math. Soc. Transl. (2). Providence (R.I.): Amer. Math. Soc., 77 (1996). – p. 159-193.

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