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arXiv:cond-mat/0107522 · Journal of Physics A Mathematical and General

Wave packet diffraction in the Kronig–Penney model

G Kälbermann

Published Jan 21, 2002• 8 citations
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Abstract

The phenomenon of wave packet diffraction in space and time is investigated numerically and analytically for a one-dimensional array of equally spaced finite-depth wells. Theoretical predictions for the lattice at long times and at low scattering energies coincide exactly with the results for a single well. At intermediate and short times compared to the classical passage time, the pattern shows both a broad diffractive pattern and an interference pattern inside each diffractive peak. The diffractive structure persists for this case to infinite time.

DOI
10.1088/0305-4470/35/4/316

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The phenomenon of wave packet diffraction in space and time is investigated numerically and analytically for a one-dimensional array of equally spaced finite-depth wells. Theoretical predictions for the lattice at long times and at low scattering energies coincide exactly with the results for a single well. At intermediate and short times compared to the classical passage time, the pattern shows both a broad diffractive pattern and an interference pattern inside each diffractive peak. The diffractive structure persists for this case to infinite time.
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Resonant transmission occurs when constructive interference results in the complete passage of an incoming wave through an array of barriers. In this paper, we explore such a scenario with one-dimensional models. We adopt wave packets with finite width to illustrate the deterioration of resonance with decreasing wave packet width and suggest an approximate wave function for the transmitted and reflected components, derived from aspects of both the wave packet and plane wave approaches. A comparison with exact numerical calculations shows excellent agreement and provides insight into the scattering process.
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