Crystal symmetries of plane-wave-like functions I. The symmorphic space groups

Abstract

A set of tables of coefficients for forming linear combinations of plane waves, both without and with spin, symmetrized with respect to all the necessary sub-groups of all 73 symmorphic space groups, is presented here. A symmetry analysis of all the Brillouin zone symmetry points of these 73 space groups is also included and serves as an index to the coefficient tables. A discussion of the method of calculation is included as well as a review of the theory which underlies the desirability of symmetrized functions, and the theory of the projection operator, by which these coefficients were calculated. Section 4, a guide to the use of the tables, may be read independently of the rest.

Work supported in part by the National Science Foundation. Submitted in partial fulfilment of the requirements for the degree of Ph.D. in physics at the University of Chicago.

Work supported in part by the National Science Foundation. Submitted in partial fulfilment of the requirements for the degree of Ph.D. in physics at the University of Chicago.

Notes

Work supported in part by the National Science Foundation. Submitted in partial fulfilment of the requirements for the degree of Ph.D. in physics at the University of Chicago.