A formula is derived which gives the exact remainder to the approximate energy eigenvalue obtained by the variation method. The remainder formula and approximations to it are closely related to the usual second-order perturbation formula. A scheme is suggested for consolidating the linear variation method and remainder formula into a single approximation method for energy eigenvalues. The method is illustrated with a calculation of the energy of the ground state of helium using 136 basis functions.
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Shull et al. (1958) studied this question.