Spectra of the Two-Electron System in the Impurity Hubbard Model
Introduction. Structure of Essential Spectrum and Discrete Spectrum of Two-Electron Triplet and Singlet States
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In this book we consider two-electron systems for the impurity Hubbard Model and investigate the spectrum of the system in a singlet state for the ni- 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 with each other. In the singlet state the appear additional two eigenvalues. In the tr...
In this book we consider two-electron systems for the impurity Hubbard Model and investigate the spectrum of the system in a singlet state for the ni- 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 with 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, consists of one-eigenvalue, consists of two eigenvalues or 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 and described the structure of essential spectrum and discrete spectrum of the energy operator of two-electron systems in an impurity Hubbard model.
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