  The study of wave packet is of great significance in quantum mechanics,
optics and fluid mechanics. However, in order to solve the strict evolution
behavior of wave packet, it is necessary not only to determine the parameters
of various physical quantities such as mass, but also to carry out the complex
integration process in configuration space and momentum space. In the final
analysis, the evolution behavior of wave packet is the evolution behavior of
distribution function parameters with time. Using the method of grey system
theory, the time-varying parameters are replaced by time-varying response
series, and then the formal structure is constructed according to the physical
meaning of time evolution to realize the approximate simulation and approximate
calculation of wave function expression. The advantage of this method is that
it can simulate the evolution of wave packet under the uncertainty of each
physical quantity. Based on the grey system theory, this paper uses GM (1,1)
model to replace the time response function of wave packet distribution,
obtains the simulated evolution behavior of wave packet wave function by means
of mathematical techniques such as variational method, and makes error analysis
and correction. In practical application, the approximate evolution behavior of
wave function can be obtained only by determining the parameters of expansion
coefficient of wave function. In this paper, the Gauss wave packet is taken as
an example to discuss the method. The grey system theory of mathematical
modeling is introduced into physical calculation for the first time, and an
approximate calculation method which can be widely used in wave packet
evolution calculation is given.
