Mathematical Physics


Spherical Harmonics and Crystals

Authors: Giuliano Bettini

The description of Point Groups is made in crystallography, among other, with "character tables". Following my classification work entitled "5 bit 32 crystal classes" and some other curious properties I've noticed, I wanted to try to find a representation with Spherical Harmonics namely: a set of 32 Spherical Harmonics each one representing a Point Group. So the purpose of this work, in a nutshell, is to combine each of the 32 crystal classes with the corresponding Spherical Harmonic that has the same symmetry properties, in a certain sense therefore a "group description". These are among all the Spherical Harmonics the only 32 with which it is possible to create periodic structures with no gaps nor overlapping. A sort of Spherical Harmonics Restriction Theorem. Other possibly interesting connections with the s p d f sub-shells, and with spin, are to be investigated.

Comments: 27 Pages. In English. Updated.

Download: PDF

Submission history

[v1] 2019-04-14 10:05:16
[v2] 2019-04-20 01:43:00
[v3] 2019-04-21 10:22:35

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