The one‐dimensional problem of electrons confined in a quadratic potential is solved in the WKB approximation. The unique feature of the problem is that, since particle bounce time is independent of energy, resonant particles that normally cause Landau damping periodically interact with the wave and regenerate all phase information. Because of the efficiency of the regeneration mechanism, the dielectric properties governing the system change and give rise to “regenerative modes” associated with harmonics at twice the bounce frequency. The eigenvalues calculated in this WKB approximation are in agreement with previous numerical calculations.