NANOSYSTEMS: PHYSICS, CHEMISTRY, MATHEMATICS, 2017, 8 (3), P. 310–316
Finiteness of discrete spectrum of the two-particle Schrödinger operator on diamond lattices
M. I. Muminov – Department of Mathematic of Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Johor, Malaysia; mukhiddin@utm.my
C. Lokman – Department of Mathematic of Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Johor, Malaysia
Department of Mathematic of Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Johor, Malaysia
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.
DOI 10.17586/2220-8054-2017-8-3-310-316