Difficulties connected to solving difference equations of hyperbolic type were analyzed in this work and discussed in detail. The results are compared to those of the standard wave equation and certain similarities were established. The method of solving the equation is generalized by means of kernel expanded into separable polynomials. The analysis was inspired by some new ideas concerning quantization of time. Two examples are given: excitons and phonons in thin crystalline films. The advanced methodology of Green's function method and the application of this new methodology resulted in a set of interesting conclusions concerning thin film properties. The significance of the obtained spatial dependence of exciton concentration was discussed and it was concluded, on the basis of the found spatial dependence of exciton concentration, that such boundary conditions of a thin molecular film which lead to high exciton concentrations can be determined. It was also concluded that thin films ...possess high superconductive properties, that physical characteristics of thin films are spatially dependent and that the spatial dependence can be the basis for widening the field of application of nanostructures.
TY - JOUR
AU - Šetrajčić, Jovan P.
AU - Jaćimovski, Stevo
AU - Sajfert, Vjekoslav D.
AU - Šetrajčić, Igor J.
PY - 2014
UR - http://jakov.kpu.edu.rs/handle/123456789/594
AB - Difficulties connected to solving difference equations of hyperbolic type were analyzed in this work and discussed in detail. The results are compared to those of the standard wave equation and certain similarities were established. The method of solving the equation is generalized by means of kernel expanded into separable polynomials. The analysis was inspired by some new ideas concerning quantization of time. Two examples are given: excitons and phonons in thin crystalline films. The advanced methodology of Green's function method and the application of this new methodology resulted in a set of interesting conclusions concerning thin film properties. The significance of the obtained spatial dependence of exciton concentration was discussed and it was concluded, on the basis of the found spatial dependence of exciton concentration, that such boundary conditions of a thin molecular film which lead to high exciton concentrations can be determined. It was also concluded that thin films possess high superconductive properties, that physical characteristics of thin films are spatially dependent and that the spatial dependence can be the basis for widening the field of application of nanostructures.
PB - Elsevier Science Bv, Amsterdam
T2 - Communications in nonlinear science and numerical simulation
T1 - Specific quantum mechanical solution of difference equation of hyperbolic type
VL - 19
IS - 5
SP - 1313
EP - 1328
DO - 10.1016/j.cnsns.2013.08.026
ER -
@article{
author = "Šetrajčić, Jovan P. and Jaćimovski, Stevo and Sajfert, Vjekoslav D. and Šetrajčić, Igor J.",
year = "2014",
url = "http://jakov.kpu.edu.rs/handle/123456789/594",
abstract = "Difficulties connected to solving difference equations of hyperbolic type were analyzed in this work and discussed in detail. The results are compared to those of the standard wave equation and certain similarities were established. The method of solving the equation is generalized by means of kernel expanded into separable polynomials. The analysis was inspired by some new ideas concerning quantization of time. Two examples are given: excitons and phonons in thin crystalline films. The advanced methodology of Green's function method and the application of this new methodology resulted in a set of interesting conclusions concerning thin film properties. The significance of the obtained spatial dependence of exciton concentration was discussed and it was concluded, on the basis of the found spatial dependence of exciton concentration, that such boundary conditions of a thin molecular film which lead to high exciton concentrations can be determined. It was also concluded that thin films possess high superconductive properties, that physical characteristics of thin films are spatially dependent and that the spatial dependence can be the basis for widening the field of application of nanostructures.",
publisher = "Elsevier Science Bv, Amsterdam",
journal = "Communications in nonlinear science and numerical simulation",
title = "Specific quantum mechanical solution of difference equation of hyperbolic type",
volume = "19",
number = "5",
pages = "1313-1328",
doi = "10.1016/j.cnsns.2013.08.026"
}
Šetrajčić, J. P., Jaćimovski, S., Sajfert, V. D.,& Šetrajčić, I. J. (2014). Specific quantum mechanical solution of difference equation of hyperbolic type.
Communications in nonlinear science and numerical simulation
Elsevier Science Bv, Amsterdam., 19(5), 1313-1328.
https://doi.org/10.1016/j.cnsns.2013.08.026
Šetrajčić JP, Jaćimovski S, Sajfert VD, Šetrajčić IJ. Specific quantum mechanical solution of difference equation of hyperbolic type. Communications in nonlinear science and numerical simulation. 2014;19(5):1313-1328
Šetrajčić Jovan P., Jaćimovski Stevo, Sajfert Vjekoslav D., Šetrajčić Igor J., "Specific quantum mechanical solution of difference equation of hyperbolic type" Communications in nonlinear science and numerical simulation, 19, no. 5 (2014):1313-1328,
https://doi.org/10.1016/j.cnsns.2013.08.026 .
