Theoretical Chemistry Accounts

, 131:1075 | Cite as

Time-dependent wave packet propagation using quantum hydrodynamics

  • Brian K. KendrickEmail author
Regular Article
Part of the following topical collections:
  1. 50th Anniversary Collection


A new approach for propagating time-dependent quantum wave packets is presented based on the direct numerical solution of the quantum hydrodynamic equations of motion associated with the de Broglie–Bohm formulation of quantum mechanics. A generalized iterative finite difference method (IFDM) is used to solve the resulting set of non-linear coupled equations. The IFDM is 2nd-order accurate in both space and time and exhibits exponential convergence with respect to the iteration count. The stability and computational efficiency of the IFDM is significantly improved by using a “smart” Eulerian grid which has the same computational advantages as a Lagrangian or Arbitrary Lagrangian Eulerian (ALE) grid. The IFDM is generalized to treat higher-dimensional problems and anharmonic potentials. The method is applied to a one-dimensional Gaussian wave packet scattering from an Eckart barrier, a one-dimensional Morse oscillator, and a two-dimensional (2D) model collinear reaction using an anharmonic potential energy surface. The 2D scattering results represent the first successful application of an accurate direct numerical solution of the quantum hydrodynamic equations to an anharmonic potential energy surface.


Wave Packet Edge Point Arbitrary Lagrangian Eulerian Move Little Square Quantum Potential 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



This work was done under the auspices of the US Department of Energy at Los Alamos National Laboratory. Los Alamos National Laboratory is operated by Los Alamos National Security, LLC, for the National Nuclear Security Administration of the US Department of Energy under contract DE-AC52-06NA25396.

Supplementary material

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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Theoretical Division (T-1, MS-B268)Los Alamos National LaboratoryLos AlamosUSA

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