NUMERICAL CALCULATION OF QUANTUM TUNNELING BASED ON JULIA

Quantum tunneling is an important model in elementary quantum mechanics. However, since solution of its wave function involves transcendental equation, many elementary quantum mechanics textbooks often focus on the explanation of transmission coefficient, and rarely mention the evolution of wave function. Although this process is mentioned in some textbooks, it is often solved by graphic method, which is not conducive to beginners' understanding of the process. In this paper, a numerical calculation method for beginners is proposed to solve this problem. According to Dirac's vectorization idea, the state vectors and operators in the Schrodinger equation are discretized in the form of vectors and matrices, respectively, and the time-dependent evolution of wave function tunneling under several potential barriers is solved by Julia numerically.