CONVERGENCE OF THE SERIES EXPANSION SOLUTION TO THE THOMAS-FERMI-DIRAC EQUATION,

Abstract

The Thomas-Fermi-Dirac statistical model has been used for approximate calculations of potential fields and charge densities. It has also been used to derive the equation of state of matter at high pressures and at various temperatures. The second-order nonlinear differential equation which results from the model can only be solved numerically. This is most accurately done by expressing the solution as a power series expanded about the origin. But beyond a certain radius the series diverges and the solution must be continued by numerical integration. It is our purpose here to study the convergence of the power series solution in order to determine precisely the region in which it is accurate. (Author)

Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1970
Accession Number
AD0712287

Entities

People

  • James E. Enstrom

Organizations

  • RAND Corporation

Tags

DTIC Thesaurus Topics

  • Charge Density
  • Convergence
  • Differential Equations
  • Dirac Equation
  • Equations
  • High Pressure
  • Nonlinear Differential Equations
  • Numerical Integration
  • Power Series

Readers

  • Fluid Dynamics.
  • Plasma Physics / Magnetohydrodynamics