Spectra of the Two-Electron System in the Impurity Hubbard Model

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 ν− 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 modelfor 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.