On the discrete spectrum of the Schrödinger operator using the 2+1 fermionic trimer on the lattice
https://doi.org/10.17586/2220-8054-2023-14-5-518-529
Abstract
We consider the three-particle discrete Schrödinger operator H; (K); K 2 T3, associated with the three-particle Hamiltonian (two of them are fermions with mass 1 and one of them is arbitrary with mass m = 1= < 1), interacting via pair of repulsive contact potentials > 0 on a three-dimensional lattice Z3. It is proved that there are critical values of mass ratios = 1 and = 2 such that if 2 (0; 1), then the operator H; (0) has no eigenvalues. If 2 ( 1; 2), then the operator H; (0) has a unique eigenvalue; if > 2, then the operator H; (0) has three eigenvalues lying to the right of the essential spectrum for all sufficiently large values of the interaction energy.
Keywords
Schrödinger operator,
Hamiltonian,
contact potential,
fermion,
eigenvalue,
quasi-momentum,
invariant subspace,
Faddeev operator
Supporting agencies: We thank unknown referee for careful reading of the manuscript and useful comments.
About the Authors
A. M. Khalkhuzhaev
V. I. Romanovsky Institute of Mathematics of the Academy of Sciences of the Republic of Uzbekistan
Uzbekistan
Uzbekistan
Ahmad M. Khalkhuzhaev
Mirzo Ulugbek 81, 100170
I. A. Khujamiyorov
Samarkand State University
Uzbekistan
Uzbekistan
Islom A. Khujamiyorov
University Boulevard 15, Samarkand 140104
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Review
For citations:
Khalkhuzhaev A.M., Khujamiyorov I.A. On the discrete spectrum of the Schrödinger operator using the 2+1 fermionic trimer on the lattice. Nanosystems: Physics, Chemistry, Mathematics. 2023;14(5):518-529. https://doi.org/10.17586/2220-8054-2023-14-5-518-529
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