Open AccessSymmetry and terrestrial spectroscopy
Author(s) -
Chao B. Feng
Publication year - 1981
Publication title -
geophysical journal of the royal astronomical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0016-8009
DOI - 10.1111/j.1365-246x.1981.tb05957.x
Subject(s) - group theory , analogy , perturbation theory (quantum mechanics) , symmetry group , symmetry (geometry) , theoretical physics , symmetry operation , irreducible representation , degeneracy (biology) , group (periodic table) , physics , spectral line , quantum mechanics , mathematics , mathematical physics , pure mathematics , geometry , bioinformatics , philosophy , linguistics , biology
Summary. There is an analogy in the algebraic structure between the terrestrial spectra belonging to different earth models and the electron energy levels of some quantum mechanical systems. The reason for such an analogy is studied by means of group theory. It is shown that the structure of the spectrum is determined solely by the symmetry of the physical system under consideration. Group theory is then applied, as a unifying theory, to study terrestrial spectroscopic problems based on the theorem that each degree of degeneracy in the spectrum is equal to the dimension of one of the irreducible representations of the symmetry group of the physical system. The influence of perturbations of lower symmetry on the degeneracies in the spectrum (particularly the pattern of splitting) is also studied through group theory; and exact results are obtained. In addition, group theory provides the selection rules for perturbation matrices which determine the coupling among normal modes belonging to the unperturbed system.