Power-Series Solutions for Energy Eigenvalues

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Abstract
A numerical method is presented for rapidly calculating the energy eigenvalues of one‐dimensional Schrödinger equations. It is applicable to systems for which the potential is either analytic or has no pole of order greater than two. The method is based on a power‐series expansion of the wave function at large distances. With the use of high‐speed computing machines the large number of terms required in the power series can be computed easily. The method is illustrated by obtaining energy eigenvalues for a number of one‐dimensional systems with potentials of the type V=kx2n/2n. It is also applicable to a variety of systems of physical interest. As an example, an exact energy eigenvalue for a rotating Morse oscillator has been calculated. This is compared with that obtained from Pekeris' approximate analytical solution.

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