A generalization of the augmented plane wave method

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Abstract
A generalization of the Augmented Plane Wave Method (APW), for band structure calculations, where continuity is not imposed on the trial wave functions is considered. Attention is called to trial functions psi which have the combination psi + lambda R2 delta n psi , of the function and its normal derivative, continuous at the surface of the APW sphere. It is shown that a study of the calculated eigenvalue as a function of the parameter lambda is very revealing because it establishes an upper and a lower bound to the true eigenvalue. It is shown that there is an ideal value of lambda for which the convergence is best.