Non-exponential and oscillatory decays in quantum mechanics

Abstract

The quantum-mechanical theory of the decay of unstable states is revisited.\nWe show that the decay is non-exponential both in the short-time and long-time\nlimits using a more physical definition of the decay rate than the one usually\nused. We report results of numerical studies based on Winter's model that may\nelucidate qualitative features of exponential and non-exponential decay more\ngenerally. The main exponential stage is related to the formation of a\nradiating state that maintains the shape of its wave function with\nexponentially diminishing normalization. We discuss situations where the\nradioactive decay displays several exponents. The transient stages between\ndifferent regimes are typically accompanied by interference of various\ncontributions and resulting oscillations in the decay curve. The decay curve\ncan be fully oscillatory in a two-flavor generalization of Winter's model with\nsome values of the parameters. We consider the implications of that result for\nmodels of the oscillations reported by GSI.\n