Abstract:
We study the position of the essential spectrum of a three-body Schrödinger operator H. We evaluate the lower boundary of the essential spectrum of H and prove that the number of eigenvalues located below the lower edge of the essential spectrum in the H model is finite.
Keywords:
essential spectrum, discrete spectrum, lower boundary of the essential spectrum, Schrödinger operator.
Citation:
Yu. Kh. Eshkabilov, R. R. Kucharov, “Essential and discrete spectra of the three-particle Schrödinger operator on a lattice”, TMF, 170:3 (2012), 409–422; Theoret. and Math. Phys., 170:3 (2012), 341–353
This publication is cited in the following 6 articles:
Kucharov R.R. Khamraeva R.R., “Non-Compact Perturbations of the Spectrum of Multipliers Given With Functions”, Nanosyst.-Phys. Chem. Math., 12:2 (2021), 135–141
Yu. Kh. Eshkabilov, R. R. Kucharov, “Partial integral operators of Fredholm type on Kaplansky–Hilbert module over L0”, Vladikavk. matem. zhurn., 23:3 (2021), 80–90
Yu. Kh. Èshkabilov, “Spectrum of a model three-particle Schrödinger operator”, Theoret. and Math. Phys., 186:2 (2016), 268–279
R. R. Kucharov, Yu. Kh. Eshkabilov, “On the number of negative eigenvalues of a partial integral operator”, Siberian Adv. Math., 25:3 (2015), 179–190
G. P. Arzikulov, Yu. Kh. Eshkabilov, “On the essential and the discrete spectra of a Fredholm type partial integral operator”, Siberian Adv. Math., 25:4 (2015), 231–242
Yu. Kh. Eshkabilov, “On the discrete spectrum of partial integral operators”, Siberian Adv. Math., 23:4 (2013), 227–233