Unitary (Normal Preserving) Methods for Solving the Schrodinger Equation with Implementation in C and C++.

Abstract

Currently, the Naval Air Warfare Center Weapons Division is exploring using the solution of the time-dependent Schrodinger for some applications in signal processing. The approach being taken to solve this problem is a difference equation. However, the solution based upon a difference equation is unstable, and the solution must be renormalized every time step. This report reviews two methods to obtain solutions that are stable and unitary (preserve the norm). Both methods are based upon the split-operator approach. One method, called the k-space method, will use the FFT, and one method, called the R-space method, will not. The k-space method is more accurate than the R-space method. However, it is a global method (because it uses the FFT), while the R-space method is local. This difference can be exploited to efficiently use the available computing architecture. Included in this report are two software packages (one in C and one in C++) that implement these methods.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1997
Accession Number
ADA323262

Entities

People

  • Fernando J. Escobar
  • Phuc Tran

Organizations

  • Naval Air Warfare Center Weapons Division

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Aerial Warfare
  • Boundaries
  • Classification
  • Computational Science
  • Computer Architecture
  • Computer Programs
  • Computing System Architectures
  • Convolution
  • Difference Equations
  • Energy
  • Equations
  • Ground State
  • Kinetic Energy
  • Personal Information Managers
  • Random Number Generators
  • Schrodinger Equation
  • Wave Functions

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Quantum spin resonance or Electron Paramagnetic Resonance spectroscopy.

Technology Areas

  • Space