Tashpulatov, S.M. (2019) The Spectrum of the Energy Operator in Three-Electron Systems with an Impurity in the Hubbard Model. The Second Doublet State. Contemporary Mathematics. Fundamental Directions, 65, 109-123.
https://doi.org/10.22363/2413-3639-2019-65-1-109-123

has been cited by the following article:

• TITLE: Spectra of the Energy Operator of Two-Electron System in the Impurity Hubbard Model

  AUTHORS: Sa’dulla Tashpulatov

  KEYWORDS: Two-Electron System, Impurity Hubbard Model, Singlet State, Triplet State, Essential Spectra, Discrete Spectrum

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.10 No.9, September 26, 2022

  ABSTRACT: We consider two-electron systems for the impurity Hubbard Model and investigate the spectrum of the system in a singlet state for the v-dimensional integer valued lattice Zv. We proved the essential spectrum of the system in the singlet state is consists of union of no more then three intervals, and the discrete spectrum of the system in the singlet state is consists of no more then five eigenvalues. We show that the discrete spectrum of the system in the triplet and singlet states differ from each other. In the singlet state the appear additional two eigenvalues. In the triplet state the discrete spectrum of the system can be empty set, or is consists of one-eigenvalue, or is consists of two eigenvalues, or is consists of three eigenvalues. For investigation the structure of essential spectra and discrete spectrum of the energy operator of two-electron systems in an impurity Hubbard model, for which the momentum representation is convenient. In addition, we used the tensor products of Hilbert spaces and tensor products of operators in Hilbert spaces and described the structure of essential spectrum and discrete spectrum of the energy operator of two-electron systems in an impurity Hubbard model.