[en] A macroscopic variable, the phase difference across a Josephson junction, is shown to obey quantum mechanics by observing the phenomena of energy-level quantization and quantum tunneling. The relevant parameters of the junction were determined in situ in the thermal regime from the dependence of the escape rate on bias current and from resonant activation in the presence of microwaves. The first observation of quantized energy levels for this system if reported. The positions of these energy levels are in quantitative agreement with the quantum-mechanical predictions based on the measured junction parameters. A model is presented that predicts correctly the observed resonance shapes. The measured value of the escape rate out of the zero-voltage state for an underdamped (Q ∼ 30) junction was found to be independent of temperature at low temperatures. This low temperature escape rate was in excellent agreement with the prediction for macroscopic quantum tunneling, with no adjustable parameters