Interaction Sensing in Dynamic Probe Microscopy

A first-order perturbative theory of the motion of a harmonic oscillator interacting with a weak arbitrary force field is presented as it pertains to dynamic force microscopy. In essence the theory corresponds to a Born approximation for the scattering of standing waves trapped in a parabolic potential. In particular it is shown that the scattering amplitudes are related to corresponding moments involving Chebyshev polynomials and associated metrics, of the conservative interaction force, and of a generalized friction coefficient accounting for irreversible interactions. Implications for dynamic force microscopy are discussed.