Interaction sensing in dynamic force microscopy

A first-order perturbative theory of the motion of a harmonic oscillator in teracting with a weak arbitrary force field is presented, as it pertains to dynamic force microscopy. In essence the theory corresponds to a Born appr oximation for the scattering of standing waves trapped in a perturbed parab olic potential. In particular, it is shown that the scattering amplitudes a re related to corresponding moments, involving Chebyshev polynomials and as sociated metrics of the conservative interaction force, and of a generalize d friction coefficient accounting for irreversible interactions. Implicatio ns for dynamic force microscopy are discussed.