The wave function is central to quantum mechanics. It contains the maximum information that can be known about a single particle's quantum state. The square of the wave function is the probability of a particle's location at any given moment. Direct imaging of a wave function used to be considered only a gedanken experiment, but became routine. An image of an atom's exact position or the movement of its electrons is almost impossible to measure because any direct observation of an atom disturbs its quantum coherence. As such, observing an atom's wave function and getting an image of its full quantum state requires many measurements to be made, which are then statistically averaged. The photoionization microscope directly visualizes atomic structure and quantum states.