TITLE:
The Structure of Essential Spectra and Discrete Spectrum of Three-Electron Systems in the Impurity Hubbard Model—Quartet State
AUTHORS:
S. M. Tashpulatov
KEYWORDS:
Essential Spectrum, Discrete Spectrum, Three-Electron System, Local Impurity States, Impurity Hubbard Model, Quartet State, Doublet State
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.9 No.6,
June
30,
2021
ABSTRACT: We consider a three-electron system in the Impurity Hubbard model with a coupling between nearest-neighbors. Our research aim consists of studying the structure of essential spectrum and discrete spectra of the energy operator of three-electron systems in the impurity Hubbard model in the quartet state of the system in a v-dimensional lattice. We have reduced the study of the spectrum of the three-electron quartet state operator in the impurity Hubbard model to the study of the spectrum of a simpler operator. We proved the essential spectra of the three-electron systems in the Impurity Hubbard model in the quartet state is the union of no more than six segments, and the discrete spectrum of the system is consists of no more than four eigenvalues.