Abstract
Abstract
We study the Schrödinger operators
H
λ
μ
(
K
)
, with
K
∈
T
2
the fixed quasimomentum of the particles pair, associated with a system of two identical fermions on the two-dimensional lattice
Z
2
with first and second nearest-neighboring-site interactions of magnitudes
λ
∈
R
and
μ
∈
R
, respectively. We establish a partition of the
(
λ
,
μ
)
−
plane so that in each its connected component, the Schrödinger operator
H
λ
μ
(
0
)
has a definite (fixed) number of eigenvalues, which are situated below the bottom of the essential spectrum and above its top. Moreover, we establish a sharp lower bound for the number of isolated eigenvalues of
H
λ
μ
(
K
)
in each connected component.
Funder
Ministry of Innovative Development of the Republic of Uzbekistan
Subject
General Physics and Astronomy,Mathematical Physics,Modeling and Simulation,Statistics and Probability,Statistical and Nonlinear Physics
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