The onedimensional infinite square well is an important model in quantum mechanics. However, its potential jumps at the boundaries, which leads to undefined derivatives of both the potential and the wave function at these points. In this paper, we start with the anharmonic oscillator model, use the finite difference method to calculate theeigenvalues and eigenfunctions of the onedimensional anharmonic oscillator, and then compare the results with the eigenfunctions and eigenvalues of the onedimensional infinite square well. We prove that the onedimensional infinite square well is the asymptotic limit of the higherorder anharmonic oscillator.