The dynamics of a diffusing particle in a potential field is ubiquitous in physics, and it plays a pivotal role in single-molecule studies. We present a formalism for analyzing the dynamics of diffusing particles in harmonic potentials at low Reynolds numbers using the time evolution of the particle probability distribution function. We demonstrate the power of the formalism by simulation and by measuring and analyzing a nanobead tethered to a single DNA molecule. It allows one to simultaneously extract all the parameters that describe the system, namely, the diffusion coefficient and the restoring-force constant.