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

In: International Conference on Mathematical Sciences and Statistics 2013

Author

Listed:
  • 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)

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.

Suggested Citation

  • Z. Muminov & F. Ismail & Z. Eshkuvatov, 2014. "On the Structure of the Essential Spectrum of Four-Particle Schrödinger Operators on a Lattice," Springer Books, in: Adem Kilicman & Wah June Leong & Zainidin Eshkuvatov (ed.), International Conference on Mathematical Sciences and Statistics 2013, edition 127, pages 187-194, Springer.
    • Handle: RePEc:spr:sprchp:978-981-4585-33-0_19
    DOI: 10.1007/978-981-4585-33-0_19
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