A time-dependent (TD), nonperturbative quantum fluid density functional equation of motion, developed in our laboratory, is numerically solved for studying the photoionization dynamics of the He atom under an intense, ultrasharp, ultrashort laser pulse. The generalized nonlinear Schrödinger equation is obtained through a hydrodynamical continuity equation and an Euler-type equation of motion. It yields the electron density, effective potential surface, and other density-based quantities from start to finish. Starting from the ground-state Hartree–Fock density for He at t = 0, various singlet and triplet states of singly and doubly excited (autoionizing) He as well as several states of He+ have been identified in the time-evolved electron density, by a Fourier transformation of the time variable of the complex autocorrelation function. Computer visualizations of the TD difference density and difference potential show distinctly nonlinear and extremely interesting geometrical features of the oscillating atom. Detailed mechanistic routes for multiphoton, sequential, and above-threshold ionization have been obtained, each route involving many states. The present, comprehensive method reveals the important physical features of the atom–laser interaction and the calculated results are consistent with current experimental and theoretical results. This emphasizes the validity of the hydrodynamical approach for studying TD quantum mechanical phenomena. © 1995 John Wiley & Sons, Inc.