ACCURATE AND STABLE NUMERICAL SOLUTIONS TO THE SCHRODINGER EQUATION,
NAVAL RESEARCH LAB WASHINGTON D C
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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 Rrho and the slope of the wave function mrho, 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 - Orho 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.
- Theoretical Mathematics
- Quantum Theory and Relativity