A New Simple Method of Simulating One Dimensional Quantum Problem Based on Lattice Point Concepts

Abstract

One-dimensional quantum problems have always been an important issue in various branches of quantum mechanics fields, and many quantum models can be idealized as one-dimensional potential profiles. Therefore, it is necessary to investigates the way to deal with and calculate the problems. This paper proposes a new and simple method for simulation and calculation of one-dimensional quantum problems. To be specific, by representing continuous X values by a series of discrete lattice points, the Hamiltonian matrix is constructed for the system in the way of dealing with monomer and many-body problems, so as to simply calculate the energy level distribution and draw the wave function image. In terms of simulating one-dimensional infinite deep potential well, one-dimensional finite deep potential well, one-dimensional multi-potential well and other one-dimensional quantum systems with this method, this paper shows that the method is accurate and practical. Compared with other methods for one-dimensional quantum problems, this paper also presents the superiority of this method. To deal with the problem based on such a method can save the computation cost and time cost, which is more convenient to study the one-dimensional quantum problem in the future. These results shed light on studying complex one-dimensional quantum problems conveniently.