Abstract
The orthogonalized plane-waves basis is used by many authors to determine the electronic states in solids, in particular in some pseudopotential methods. However, this O.P.W. basis has the great inconvenience of being overcomplete. To avoid this difficulty, we construct an orthonormalized and complete basis following Girardeau's idea. Then, we show that the initial eigenvalue problem is equivalent to the eigenvalue problem related to a certain pseudo-equation. The removal of the partial indeterminacy initially introduced in the definition of our basis allows us to solve the problem by perturbation expansion from the plane-wave states with good convergence.
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