We present a new method for numerical integration of the radial electronic Schrödinger equation with these characteristics: (i) it uses a quantity directly related to the logarithmic derivative of the wave function, thereby facilitating the matching of solutions obtained for different radial regions; (ii) it avoids difficulty from the singularity of the logarithmic derivative at the nodes of the wave function; and (iii) it takes appropriate cognizance of the asymptotic form of the wave function at infinite radius. Examples are presented showing that eigenvalues can be obtained by the new method by outward integration alone, but that a combination of inward and outward integration leads to efficiencies which compare favorably with those achievable by the most popular previously existent method, that of Numerov.

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1988
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