Highly Oscillatory Behavior Of Numerical Solutions Of Space Fractional Semi-classical Schr(?)dinger Equation

Schr(?)dinger equation is also known as Schr(?)dinger wave equation,it is a basic equation in the field of quantum mechanics,its position in quantum mechanics is equivalent to that of Newton equation in classical mechanics.The classical Schr(?)dinger equation is a second-order partial differential equation established by combining the concept of matter waves with the wave equation,which can be used to describe the movement of microscopic particles.The semi-classical Schr(?)dinger equation studied in this paper has important significance in both quantum physics and theoretical chemistry.Among them,the high oscillation characteristic of the solution is the main problem of our research.This paper first introduces the physical background of the semi-classical Schr(?)dinger equation and the definition method of the fractional Laplace operator.The effects of integer-order semiclassical Schr(?)dinger equations and fractional-order semiclassical Schr(?)dinger equations on the highly oscillatory behavior of solutions under different conditions are introduced,and numerical algorithms are given.Finally,numerical examples are given.The angle indicates the correctness of the theoretical results.In this paper,we mainly use Strong splitting Fourier spectral method and Magnus–Zassenhaus splitting method to study highly oscillatory behavior of solutions of space fractional semi-classical Schr(?)dinger equation.Compared with the highly oscillatory behavior of integer order,it turns out that this highly oscillatory behavior applies to fractional Schr(?)dinger equations as well,and the small parameter and the potential function (1(,)have a direct impact on the highly oscillatory behavior of the spatial fractional Schr(?)dinger equation under different in some cases.