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Computational Investigation of Wave Packet Scattering in the Complex Plane: Propagation on a Grid
Robert E Wyatt1, Brad A Rowland1
1Department of Chemistry and Biochemistry, University of Texas, Austin, Texas 78712.
Journal of Chemical Theory and Computation
|November 27, 2015
Summary
This study computationally investigates wave packet scattering from a Gaussian barrier using complex plane analysis. Ripples in the reflected packet cause interference oscillations, while the sub-real axis component contributes to transmission.
Area of Science:
- Quantum mechanics
- Computational physics
- Wave packet dynamics
Background:
- Investigating quantum phenomena requires advanced computational methods.
- Understanding wave packet behavior is crucial for quantum scattering theory.
Purpose of the Study:
- To computationally investigate the time-dependent scattering of a wave packet from a Gaussian barrier in the complex z-plane.
- To analyze the role of ripples and sub-real axis components in wave packet scattering.
- To visualize and interpret quantum mechanical functions like the quantum momentum function (QMF) and quantum action function.
Main Methods:
- Analytic continuation of wave packet and potential energy functions.
- Two-dimensional grid propagation of the wave packet.
- Plotting of wave packet density, real part, QMF, Pólya vector field, and quantum action function.
- Analysis of vorticity for nonanalyticity detection.
Main Results:
- Ripples (quasi-nodes) above the real axis in the reflected packet cause interference oscillations upon crossing.
- The component of the wave packet below the real axis significantly contributes to the transmitted packet.
- QMF vector maps reveal hyperbolic flow around quasi-nodes and circular flow around stagnation points.
- Pólya vector field analysis shows circular flow near quasi-nodes, and vorticity helps pinpoint QMF nonanalyticity.
Conclusions:
- Complex plane analysis provides insights into wave packet scattering dynamics.
- Interference oscillations arise from quasi-nodes moving across the real axis.
- The Pólya vector field and its vorticity are valuable tools for understanding quantum mechanical field behavior and nonanalyticities.
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