The spectrum of position fluctuations of a Brownian particle bound in a harmonic trap near a plane wall is calculated from an approximate result for the Fourier transform of the velocity autocorrelation function. Both a no-slip and a perfect slip boundary condition at the wall are considered. In both cases at low frequency the calculated spectrum differs markedly from recent experimental data. It is suggested that a partial slip boundary condition with a frequency-dependent slip coefficient may explain the experimental results.
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