Scattering Problems via Real-time Wave Packet Scattering

• URL: http://arxiv.org/abs/2103.01027v2
• Date: Sat, 13 Mar 2021 15:24:08 GMT
• Title: Scattering Problems via Real-time Wave Packet Scattering
• Authors: M. Staelens and F. Marsiglio
• Abstract summary: We do this by using the wave packet approach to scattering, which presents a more intuitive physical picture than the traditional plane wave approach. We present several short simulations of the scattering process which emphasize how a simple methodology can be used to visualize some remarkable phenomena.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this paper, we use a straightforward numerical method to solve scattering models in one-dimensional lattices based on a tight-binding band structure. We do this by using the wave packet approach to scattering, which presents a more intuitive physical picture than the traditional plane wave approach. Moreover, a general matrix diagonalization method that is easily accessible to undergraduate students taking a first course in quantum mechanics is used. Beginning with a brief review of wave packet transport in the continuum limit, comparisons are made with its counterpart in a lattice. The numerical results obtained through the diagonalization method are then benchmarked against analytic results. The case of a resonant dimer is investigated in the lattice, and several resonant values of the mean wave packet momentum are identified. The transmission coefficients obtained for a plane wave incident on a step potential and rectangular barrier are compared by investigating an equivalent scenario in a lattice. Lastly, we present several short simulations of the scattering process which emphasize how a simple methodology can be used to visualize some remarkable phenomena.

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