We begin with a brief review of Fourier series. Any periodic function of interest in physics can be expressed as a series in sines and cosines—we have already seen that the quantum wave function of a ...We begin with a brief review of Fourier series. Any periodic function of interest in physics can be expressed as a series in sines and cosines—we have already seen that the quantum wave function of a particle in a box is precisely of this form. The important question in practice is, for an arbitrary wave function, how good an approximation is given if we stop summing the series after N terms.