The oft-used log-normal distribution for solving many population-balance problems is in fact a degenerate case of a Hermite function expansion of the solution in log particle-size coordinate. Corrective capabilities of such an expansion constitute vast improvements not only over those using the log-normal distribution, but also over discretization methods in that moments other than those designed for in the latter are predicted with much higher accuracy, although at greater computational cost. The Hermite spectral method is compared with known analytical results and other computational techniques for particle dynamic processes involving agglomeration, breakage, and growth. This method is extremely accurate and flexible, as evidenced by the wide range of problems it can solve, both transient and steady state, along with perfectly mixed or convection dominant problems. Particle distributions are allowed to evolve according to the physics of the process, not constrained by restrictive assumptions inherent in the prespecified form of the distribution.