The point spectrum of the three-particle Schr ¨odinger operator for a system comprising two identical bosons and one fermion on Z.
https://doi.org/10.17586/2220-8054-2024-15-4-438-447
Abstract
We consider the Hamiltonian of a system of three quantum particles (two identical bosons and a fermion) on the one-dimensional lattice interacting by means of zero-range attractive or repulsive potentials. We investigate the point spectrum of the three-particle discrete Schrödinger operator H(K), K ∈ T which possesses infinitely many eigenvalues depending on repulsive or attractive interactions, under the assumption that the bosons in the system have infinite mass
Keywords
Schr ¨odinger operator,
dispersion functions,
zero-range pair potentials,
discrete spectrum,
essential spectrum
Supporting agencies: The authors acknowledge support from the Innovative Development Agency of the Republic of Uzbekistan (Grant No. FZ–20200929224), and they thank the anonymous referee for reading the manuscript carefully and for making valuable suggestions.
About the Authors
Z. I. Muminov
Tashkent State University of Economics; Institute of Mathematics named after V.I.Romanovsky
Uzbekistan
Uzbekistan
Zahriddin I. Muminov
100066, Tashkent; 100174, Tashkent
V. U. Aktamova
Samarkand Institute of Veterinary Medicine
Uzbekistan
Uzbekistan
Vasila U. Aktamova
140103, Samarkand
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Review
For citations:
Muminov Z.I., Aktamova V.U. The point spectrum of the three-particle Schr ¨odinger operator for a system comprising two identical bosons and one fermion on Z. Nanosystems: Physics, Chemistry, Mathematics. 2024;15(4):438-447. https://doi.org/10.17586/2220-8054-2024-15-4-438-447
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