On The Spectrum

BI Si-wen

At first this paper summarizes the current situation and historical development of the spectrum research, the difficulties and demand background. Then it introduces the research status of quantum spectrum and research ideas of energy distribution in quantum spectrum. We explain the concept of quantum spectrum, the difference between quantum spectrum and spectrum. We elaborate energy distribution in quantum spectrum from three aspects, which are representation, feature and mechanism of quantum spectrum energy distribution. Finally we describe the application of monochrome quantum spectrum about imaging and detection aspects and give an overview of the quantum spectrum. Based on above research results we continue to study and achieve the detection of multi-spectral imaging, which provide the technical basis for the application. We try access to an advanced stage of quantum spectrum study as soon as possible.

Victor S. Ibáñez

Jennifer Gold

Sadulla Mamarazhabovich Tashpulatov, R. T. Parmanova

We consider the energy operator of four-electron systems in the Hubbard impurity model and investigate the structure of the essential spectrum and discrete spectra for the second singlet state of the system. It is shown that in the one-dimensional and two-dimensional cases the following situations exist for the essential and discrete spectrum: (a). the essential spectrum of the operator of the second singlet state of four electrons in the Hubbard impurity model consists of a union of eight segments, and the discrete spectrum of the operator consists of six eigenvalues; (b). the essential spectrum of the operator consists of a union of sixteen segments, and the discrete spectrum of the operator consists of fourteen eigenvalues; (c). the essential spectrum of the operator consists of a union of thirteen segments, and the discrete spectrum of the operator consists of nine eigenvalues; (d). the essential spectrum of the operator consists of a union of three segments, and the discrete spectrum of the operator consists of three eigenvalues. In the three-dimensional case the following situations arise: (a). the essential spectrum of an operator consists of unions of eight segments, and the discrete spectrum of the operator consists of six eigenvalues, or the essential spectrum of an operator consists of unions of three segments, and the discrete spectrum of the operator consists of three eigenvalues; (b). the essential spectrum of an operator consists of unions of eight segments, and the discrete spectrum of the operator consists of six eigenvalues; (c). the essential spectrum of an operator consists of unions of sixteen segments, and the discrete spectrum of the operator consists of fourteen eigenvalues; (d). the essential spectrum of an operator consists of unions of three segments, and the discrete spectrum of the operator consists of three eigenvalues.

Sadulla Mamarazhabovich Tashpulatov

We consider the energy operator of six-electron systems in the Hubbard model and study the structure of the essential spectrum and the discrete spectrum of the system for the second singlet state of the system. In the one- and two-dimensional cases, it is shown that the essential spectrum of the six-electron second singlet state operator is the union of seven closed intervals, and the discrete spectrum of the system consists of a single eigenvalue lying below (above) the domain of the lower (upper, respectively) edge of the essential spectrum of this operator. In the three-dimensional case, there are the following situations for the essential and discrete spectra of the six-electron second singlet state operator: (a) the essential spectrum is the union of seven closed intervals, and the discrete spectrum consists of a single eigenvalue; (b) the essential spectrum is the union of four closed intervals, and the discrete spectrum is empty; (c) the essential spectrum is the union of two closed intervals, and the discrete spectrum is empty; (d) the essential spectrum is a closed interval, and the discrete spectrum is empty. Conditions are found under which each of the situations takes place.

Stephen J. Gustafson, Israel Michael Sigal