The Strategy for Time Dependent Quantum Mechanical Calculations Using a Gaussian Wave Packet Representation of the Wave Function.

Abstract

We develop methodology for performing time dependent quantum mechanical calculations by representing the wave function as a sum of Gaussian wave packets (GWP), each characterized by a set of parameters such as width, position, momentum and phase. The problem of computing the time evolution of the wave function is thus reduced to that of finding the time evolution of the parameters in the Gaussians. This parameter motion is determined by minimizing the error made by replacing the exact wave function in the time dependent Schroedinger equation with its Gaussian representation approximant. This leads to first order differential equations for the time dependence of the parameters, and those describing the packet position and the momentum of each packet have some resemblance with the classical equations of motion. The paper studies numerically the strategy needed to achieve the best GWP representation of time dependent processes.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1985
Accession Number
ADA152709

Entities

People

  • Bret Jackson
  • Horia Metiu
  • Robert Heather
  • Shin-ichi Sawada

Organizations

  • University of California, Santa Barbara

Tags

Communities of Interest

  • Energy and Power Technologies
  • Weapons Technologies

DTIC Thesaurus Topics

  • Absorption
  • Absorption Cross Sections
  • Chemistry
  • Computational Science
  • Differential Equations
  • Diffraction
  • Dynamics
  • Equations Of Motion
  • Integrals
  • Kinetic Energy
  • Military Research
  • Molecular Mechanics Methods
  • Probability
  • Quantum Mechanics
  • Scattering
  • Trajectories
  • Uncertainty Principle

Fields of Study

  • Physics

Readers

  • Approximation Theory.
  • Fluid Dynamics.
  • Fluid Mechanics and Fluid Dynamics.

Technology Areas

  • Quantum Computing