Method of own forms for determination of separate bands


  • A. Morozov



individual spectral bands, crystalline phosphors, Gaussian function, eigenmode decomposition


The problem of determining the separate bands of the phosphor photoluminescence spectrum described by the Gaussian function is solved by the method of decomposition into its own forms. This allows you to calculate two parameters of each band: amplitude and variance. An example is the photoluminescence spectrum of a ZnS:Mn single crystal. It consists of five separate bands. Two systems of fifth-order equations linear for one parameter of each band are obtained. This parameter is generalized and is equal to the product of the amplitude and the root of the variance. The coefficients of these systems depend on the second parameter. This non-linear parameter is related to variance. In order to simplify the two systems, the problem is solved in several stages. Based on the analysis of literary sources, the two largest bands are selected. In addition, the origin of coordinates is well chosen. This allows us to simplify both systems and completely determine the parameters of each of the largest bands from the systems of second-order equations. As a result of these simplifications, the order of the two systems and the parameters of the other three bands are reduced. Thus, the problem is reduced to solving a system of the second and third order nonlinear equations.


Poluchenie nanokristallov ZnS metodom samorasprostranyayuschegosya vyiso-?otemperaturnogo sinteza / M. F. Bulanyi, A. V. Kovalenko, A. S. Morozov, [ta in.] // Zhurnal nano- ta elektronnoyi fiziki. - 2017. - T. 9, #2, S. 02007-1 – 02007-4.

Chebyishev P. L. Teoriya veroyatnostey / Pafnutiy Lvovich Chebyishev - M.,L.: Izd-vo AN SSSR, 1936. — 252 s.