Transformation of Fractional Quantum Mechanical Kernel in the Infinite Square Well

摘要

Fractional quantum mechanics kernel is a kind of wave function, which can describe the evolution process of fractional quantum system. In this paper, we study the Laplace transformation, energy-time transformation and momentum representation of free particle quantum mechanics kernel in infinite square well. Firstly, we obtain the Laplace transformation of quantum mechanical kernel by using the Fox’s H function representation of free particle quantum mechanics kernel in the infinite square well, and then use Path integral form of quantum mechanics kernel to calculate its energy-time transformation and momentum representation. The transformation of quantum mechanics kernel can simplify the calculation results in fractional quantum mechanics, so as to study its properties better.