Structure of essential spectra and discrete spectrum of the energy operator of four-electron systems in the impurity Hubbard model. Quintet state. One-dimensional case

We consider the energy operator of four electron systems in the impurity Hubbard model and investigated the structure of essential spectra and discrete spectrum of the system
in the quintet state of the system. It is shown that there are such situations:
a). the essential spectrum of the four-electron quintet state operator is consists of the union of four segments, and the discrete spectrum of the four-electron quintet state operator is consists of single eigenvalue;
b). the essential spectrum of the four-electron quintet state operator is consists of the union of ten segments, and the discrete spectrum of the four-electron quintet state operator is consists of five eigenvalues;
c). the essential spectrum of the four-electron quintet state operator is consists of single segment, and the discrete spectrum of the four-electron quintet state operator is empty set;
Provided that every situation occurs. Found the conditions, when every situation to take place.

Keywords: Impurity Hubbard model, four-electron system, essential spectra, discrete spectrum, quintet state, triplet state, singlet state