On Resonance: A First Glance into the Behavior of Unstable States

Dynamical processes in nature often involve unstable states. Analyzing systems with a finite lifetime can be challenging for a practitioner of quantum mechanics. To study such processes in a quantum system, one must venture into the continuum where the use of a continuous superposition of states, i.e., a wave packet, is required. Most of our quantum education focuses on quantized bound states rather than on the behavior of wave packets. Here, we aim to give a pedagogic introduction to the behavior and analysis of unstable states. To achieve this, we introduce two complementary viewpoints by which such states can be analyzed. We further discuss the physical mechanisms through which quantum unstable states are formed.