Diffusing particle in a potential field is a fundamental process in a lot of physical systems. Although in some cases the steady-state solution is sufficient, the dynamic characteristics are important for many others.

We present formalism that allows to fully characterizing the dynamics of a diffusing particle in a harmonic potential. It is based on the solution of Smoluchowski equation for harmonic potential field and allows us to find the particle's diffusion coefficient and the potential effective spring-constant simultaneously.

Interestingly, these dynamic properties were not yet fully explored, although they can be important for a vast number of single-molecule experiments.

To test this formalism we performed computer simulations and tethered particle motion (TPM) experiments. In TPM experiment, one end of a DNA molecule is attached to a surface while its other end attached to a sub-micron bead. Due to the spring-like properties of the DNA, this system is an excellent realization for a diffusing particle in a harmonic potential.

We believe that our formalism has a great potential for analyzing the dynamics of various single-molecule experiments such as optical tweezers, magnetic tweezers and TPM.