A Comment on p-Orbital Bands and Crystal Structure

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Why is a certain crystalline structure preferred to others in each element substance? This question seems to be a still difficult problem within the framework of the present solid state physics, in spite of the success of the band theory. One should, however, find out the origin which stabilizes the structure of the aggregate of atoms in the properties of individual constituent atoms. The aim of this paper is to report on an idea of our attempt to construct a primitive understanding of this problem on the basis of an idealized model Let us consider a system consisting of one kind of atoms each of which has only a set of p-levels with three-fold degeneracy. It is allowed to regard the p-state as a three dimensional vector, because the angular relations of any two p-states both in the configuration space and in the Hilbert space coincide each other: If the p-state with the angular wave function V3/4i-(J"·e) /lrl is denoted by the ket ]e), then

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