M. I. Muminov, C. Lokman, “Finiteness of discrete spectrum of the two-particle Schrödinger operator on diamond lattices”, Nanosystems: Physics, Chemistry, Mathematics, 2017, Volume 8, Issue 3,Pages <nobr>310

MATHEMATICS

Finiteness of discrete spectrum of the two-particle Schrödinger operator on diamond lattices

M. I. Muminov, C. Lokman

Department of Mathematic of Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Johor, Malaysia

Abstract: We consider a two-particle Schrödinger operator $H$ on the $d$-dimensional diamond lattice. We find a sufficiency condition of finiteness for discrete spectrum eigenvalues of $H$.

Keywords: two-particle Hamiltonian on lattice, Birman–Schwinger principle, discrete spectrum.

Received: 21.03.2017
Revised: 05.05.2017

Language: English

DOI: 10.17586/2220-8054-2017-8-3-310-316