Proceeding from the pseudopotential-well approximation for ion motion in a quadrupole ion trap, mathematical expressions are derived to describe the excitation amplitude of an ion packet at a given mass-to-charge ratio. Ion-neutral collisions are incorporated to describe the damping of ion trajectories and to describe the distribution of individual ion trajectories about a mean amplitude for the ion packet. The rate of increase of the amplitude during scanning is related to expressions that describe the amplitude dispersion of the ions at the time of ejection from the trap, which is operating in a resonance ejection scanning mode to describe the temporal line width of the ejected ion packet. The temporal line width is related to mass resolution under a number of different scanning conditions. Included in the discussion are considerations of the effect on resolution of the resonance excitation voltage, temperature, pressure, noise, and buffer-gas composition. An expression for the maximum possible resolution at high ion mass-to-charge ratios is developed, and these results are compared to an existing theoretical construction. The expressions derived under the pseudopotential-well approximation are further extended to high q z values and compared to experimental data previously published by two other researchers.