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arXiv · 1206.0292

Matrices, bases and matrix elements for cubic double crystallographic groups

Oleg Chalaev
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Abstract

Matrices of the irreducible representations of double crystallographic point groups O, Td, Ox{1,I} and Tdx{1,I} are derived. The characteristic polynomials (spinor bases) up to the sixth power are obtained. The method for the derivation of the general form of an arbitrary matrix element of a vector/tensor quantity is developed; as an application, the kp matrix elements are calculated. It is demonstrated that the other known method for obtaining the bases of the irreducible representations of the double groups (LS-diagonalization of a linear combination of spherical harmonics) is unreliable.

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Oleg Chalaev. 2012-06-13. Matrices, bases and matrix elements for cubic double crystallographic groups. https://arxiv.org/abs/1206.0292

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