We present a quantum mapping for the kicked harmonic oscillator which relates the probability amplitudes of the undriven oscillator's eigenfunctions over successive kicks. We show how for various kick strengths the wave functions lave a linear energy increase up to the limit imposed b y the finite matrix size of the evolution matrix. We use this linear energy increase to define a quantum diffusion-like coefficient. We also show how this increase in energy causes the wave functions to spread out and become diifuse with fittle or no discernible structure. This model may serve as a paradigm for the study of quantum chaos.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.