Accession Number : AD0655439

Title :   ACCURATE AND STABLE NUMERICAL SOLUTIONS TO THE SCHRODINGER EQUATION,

Corporate Author : NAVAL RESEARCH LAB WASHINGTON D C

Personal Author(s) : Rouse,Carl A.

Report Date : 23 JUN 1967

Pagination or Media Count : 28

Abstract : A new method has been presented for accurate and stable numerical solutions of ordinary differential equations. Applied to the Schrodinger equation the two essential features of the method are (a) simultaneous Taylor expansions between space steps delta rho of the wave function R(rho) and the slope of the wave function m(rho), and (b) the derivation of initial values through either an exact series solution of the Schrodinger equation valid at or near the origin, or through an approximate analytical solution valid for all n and l to terms of order rho superscript 2 - O(rho superscript 2). As far as the author can determine, the present results represent the first known accurate and stable numerical solutions of the radial hydrogenic Schrodinger equation. With the present ability to calculate eigenvalues to nine or more significant figures and eigenfunctions to nine or more decimal places, the present method becomes an alternative to perturbation and variational methods.

Descriptors :   (*PARTIAL DIFFERENTIAL EQUATIONS, *QUANTUM THEORY), (*NUMERICAL ANALYSIS, PARTIAL DIFFERENTIAL EQUATIONS), TAYLOR'S SERIES, HYDROGEN, TRANSFORMATIONS(MATHEMATICS), WAVE FUNCTIONS, BOUNDARY VALUE PROBLEMS

Subject Categories : Theoretical Mathematics
      Quantum Theory and Relativity

Distribution Statement : APPROVED FOR PUBLIC RELEASE