This paper presents a numerical simulation study of a multi-particle quantum system in a one-dimensional infinite potential well using COMSOL Multiphysics software by developing a parameterized dimension mapping strategy. By establishing a non-separable correspondence between particle coordinates and the built-in spatial dimensions of the software, the computational complexity of high-dimensional quantum systems is overcome. The analysis of single-electron, two-electron, and three-electron systems reveals the impact of Coulomb inter actions on the wave function distribution and energy level structure. It is found that in the two-electron system, Coulomb interaction concentrates the probability density of the wave function in regions where the electrons are farther apart and significantly increases the total energy of the system. For different numbers of electrons, the energy-width dependence relationship (the rule of how the ground state energy changes with the width of the potential well) can be divided into contributions from kinetic and potential energy. The former is inversely proportional to the square of the potential well width, while, the latter is inversely proportional to the first power of the potential well width. By introducing effective power analysis, it is discovered that as the number of electrons increases, the relationship between energy and potential well width tends to be inversely proportional in a linear manner. This methodological innovation significantly reduces the difficulty of teaching demonstrations of multi-body quantum systems, and the research findings provide a new perspective for a deeper understanding of the effects of electron interactions in low-dimensional quantum systems.