With the interest in quantum structures, there is a need to have a flexible method that can help us to determine
eigenfunctions for these structures. In this article, we present a method that accomplishes this by using the simulation of
the Schrödinger equation based on finite-difference time-domain (FDTD). We choose one-and two-dimensional finite
square well potential, and one-and two-dimensional harmonic oscillator potential as examples. Giving the initial
condition, we determine the eigenfrequencies through a Fourier transform of the time domain data collected at the center
point in the problem space. Another simulation implements a discrete Fourier transform at the eigenfrequencies at every
point in the problem space, hence, the eigenfunctions can be constructed.