Hitting a Ball on a Spring: A Simple Model for Understanding Decoherence with Wavefunctions


The typical approach to studying decoherence begins by examining a combined system and interacting environment (termed bath), and then deriving a master equation to examine the behavior of the density matrix after tracing over the bath, typically by invoking the Markovian approximation. This approach is quite successful for a large variety of systems however is frequently a non-intuitive picture that can mask the fundamental behavior of the system. We examine here a simple model that captures the essence of decoherence and study it using the wavefunction picture, invoking the analytic concepts of the correspondence principle, the method of images, the phase jitter concept, and the scattering matrix formalism. We complement this with a numerical study using the split operator FFT method, the forced harmonic oscillator method, and the thawed Gaussian approximation.

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