PROGRAMMING THE IBM 701 COMPUTER FOR DOUBLE NUMERICAL INTEGRATION OF THE OVERLAP INTEGRAL. BETWEEN TWO HYDROGEN-LIKE WAVE FUNCTIONS
Creators:Villars, D. S.
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Publisher:Ohio State University
The 701 Computer has been programmed to derive, to 10-decimal-digit accuracy, the coefficients of the polynomial terms representing hydrogen-like wave functions. The results from this computation are recorded on punched cards, and then used as data input for a second program which computes the values of the individual polynomials, multiplies them together with the volume element for polar coordinates, and supplies the product as the integrand for a double numerical quadrature over radial distance and polar angle. Subtraction of the ""Simpson"" error, used to define the (adjustable) interval of integration, from the computed value of the integral, effects the removal of error terms up to (but excluding) the sixth derivative. This amounts to fitting groups of five points by quartic equations. A study has been made of dependence of speed of the double integration on maximum Simpson error specification.
Author Institution: U. S. Naval Ordnance Test Station
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