Solutions of extended supersymmetric matrix models for arbitrary gauge groups

Energy eigenstates for N=2 supersymmetric gauged quantum mechanics are found for the gauges groups SU(n) and U(n). The analysis is aided by the existence of an infinite number of conserved operators. The spectum is continuous. Eigenstates at zero coupling for N>2 are also presented, a case which is relevant for the conjectured description of M theory in the infinite momentum frame.