English

Matrices, bases and matrix elements for cubic double crystallographic groups

Materials Science 2012-06-14 v3

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.

Keywords

Cite

@article{arxiv.1206.0292,
  title  = {Matrices, bases and matrix elements for cubic double crystallographic groups},
  author = {Oleg Chalaev},
  journal= {arXiv preprint arXiv:1206.0292},
  year   = {2012}
}

Comments

test.nb corrected. All matrices of the irreducible representations together with the transformation parameters are contained in the source of the article

R2 v1 2026-06-21T21:13:14.987Z