The single particle spectrum of an electronic system is a measure of the ease of inserting a single, whole electron into the system at a particular energy. A peak in this spectrum indicates that there is a long-lived state available for electrons at that particular energy — in essence, that it is possible to form a quasiparticle at that energy. By revealing the energies of the quasiparticles, these spectra teach us about the many-body ground state of the system. However, experimental difficulties have prevented the measurement of this spectrum in two dimensional electron systems until recently. I will present tunneling measurements of the single particle spectrum of a 2D system in a Gallium Arsenide quantum well performed using a novel pulsed technique called timed domain capacitance spectroscopy. These spectra provide a uniquely intuitive view of the integer and fractional quantum Hall effect, shedding light on a variety of previously unobserved phenomena including direct and indirect exchange splittings, coupled electron-plasmon modes, and Landau levels of composite fermions.