On the Structure of the Essential Spectrum of Four-Particle Schrödinger Operators on a Lattice

Z. Muminov (), F. Ismail () and Z. Eshkuvatov ()
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Z. Muminov: University Putra Malaysia, Department of Mathematics, Faculty of Science
F. Ismail: University Putra Malaysia, Department of Mathematics, Faculty of Science
Z. Eshkuvatov: University Putra Malaysia, Department of Mathematics, Faculty of Science

A chapter in International Conference on Mathematical Sciences and Statistics 2013, 2014, pp 187-194 from Springer

Abstract: Abstract The four-particle discrete Schrödinger operator $H(K),$ $K\in ({-}\pi,\pi]^3$ corresponding to the system of the four particles on the lattice $\mathbb{Z}^3$ with arbitrary “dispersion functions” not necessarily having compact support and interacting via short-range pair potentials, is described in the coordinate representation as bounded self-adjoint operator on the corresponding Hilbert space. We describe the location and structure of the essential spectrum of the four-particle discrete Schrödinger operator $H(K),$ $K\in ({-}\pi,\pi]^3$ by means of the spectrum of the three-particle discrete Schrödinger operators and establish the resolvent equation.

Keywords: Essential Spectrum; Resolvent Equation; Short-range Pair Potentials; Dispersion Function; Finite Rank Residues (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-981-4585-33-0_19

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DOI: 10.1007/978-981-4585-33-0_19

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