Application of Grey System Theory in Approximate Calculation of Wave Packet Evolution

doi:10.19596/j.cnki.1001-246x.8361

Abstract

Abstract:

Based on the grey system theory, we replace the time response function of GM (1, 1) model for wave packet distribution, and obtain simulated evolution behavior of wave packet's wave function with mathematical techniques such as variational method, and make error analysis and correction. In practical applications, the approximate evolution behavior of wave function can be obtained with parameters of its development coefficient. Gaussian wave packet is taken as an example to show the method. The grey system theory in mathematical modeling is introduced into the calculation of physics, and an approximate calculation method is provided, which can be used in the calculation of wave packet evolution.

Key words: wave packet, evolution, grey system, mathematical modeling

Jiayu NI, Dehong GAO, Linfeng YE, Xiangdong FENG. Application of Grey System Theory in Approximate Calculation of Wave Packet Evolution[J]. Chinese Journal of Computational Physics, 2022, 39(2): 201-211.

Figures/Tables 8

Fig.1 A schematic of relative error function of the variance

Fig.2 Wave function of a photon in which the part falling in the interval [-1000, 1000] is 99.8% of the whole

Fig.3 Relative error functions of gray wave function and wave function at 0, 300, 500, 1000 m

Fig.4 (a) The effective time decreases rapidly as the development factor α increases; (b) The average relative error in effective time decreases continuously as the development factor α increases

Fig.5 Comparison between gray wave function and wave function (The fatter and shorter wave packets are described with the gray wave function over time.)

Fig.6 The relative error of φG and φ at the final moment of effective time t=95.43 s

Fig.7 Relative error function of Kawahara wave

Fig.8 The figure of fit effect (The red markers are data points. The blue and green lines are fit functions.)

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