本文针对相对论性氢原子系统，从狄拉克方程出发，严格求解出了氢原子电子的相对论性波函数解.在此基础上，采用蒙特卡罗模拟方法对氢原子的电子云密度进行了抽样，并利用Mathematica软件实现了相对论条件下的氢原子中具有自旋的电子云的三维可视化.分析了不同主量子数、轨道角动量量子数和磁量子数下的电子云分布，并对相对论和非相对论情况下的电子云形态进行了对比说明.此外，本文还提出了一种基于舍选法和轮盘赌抽样法的电子云抽样算法，可有效应用于一般具有自旋的原子系统电子云可视化.

 This paper focuses on the relativistic hydrogen atom system. Starting from the Dirac equation, the relativistic wave function of the electron of the hydrogen atom is strictly solved. On this basis, the MonteCarlo simulation method is adopted to sample the probability cloud density of the electron, and the threedimensional visualization of the probability cloud of the electron with spin in the hydrogen atom under relativistic conditions is realized by using Mathematica software. The electron cloud distribution under different principal quantum numbers, orbital angular momentum quantum numbers and magnetic quantum numbers is analyzed, and the electron cloud morphology under relativistic and non-relativistic conditions is compared. In addition, this paper proposes a probability cloud sampling algorithm based on the acceptance rejection sampling method, which can be effectively applied to the visualization of the electron cloud of general atomic systems with spin.