CRITERIA FOR SCHROEDINGER SEPARABILITY APPLIED TO SATELLITE ORBIT THEORY

Abstract

Certain criteria for separating the Schroedinger wave equation of quantum mechanics will also permit separation of the Hamilton-Jacobi equation of classical mechanics. In particular, a potential which leads to separability under these criteria must have the same functional form for either equation. The most general axially symmetric gravitational potential which permits Hamilton-Jacobi separability in spherical coordinates is found to be the sum of the zeroth and first spherical harmonics. This result is discussed in relation to several other gravitational potentials which have been used in artificial satellite orbit studies. (Author)

Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1962
Accession Number
AD0289685

Entities

People

  • G.b. Findley
  • P.m. Fitzpatrick

Organizations

  • Air Armament Center

Tags

Communities of Interest

  • Space

DTIC Thesaurus Topics

  • Artificial Satellites
  • Differential Equations
  • Equations
  • Mechanics
  • Molecular Mechanics Methods
  • Orbits
  • Partial Differential Equations
  • Quantum Mechanics
  • Satellite Orbits
  • Spherical Harmonics
  • Wave Equations

Fields of Study

  • Physics

Readers

  • Calculus or Mathematical Analysis
  • Space Exploration and Orbital Mechanics.

Technology Areas

  • Quantum Computing
  • Space
  • Space - Orbital Debris