In most approaches to teaching quantum mechanics, discrete energy levels are introduced through the
example of the infinite square well. Here, the boundary conditions at the walls, namely a vanishing
amplitude of the wave function, lead to quantized energy levels. This contribution extends the
discussion to more realistic, smooth potentials in one dimension, including non-symmetric
potentials. A numerical solution algorithm for the corresponding time-independent Schr?dinger
equation illustrates quantization in an intuitive manner by use of simple forward-shooting and
bisection methods. It also demonstrates how computational physics can go beyond finding approximate
solutions to a specific problem and truly aid the understanding of a basic concept in physics.