Mathematics
Scientific paper
Jul 1985
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1985rpph...48..907j&link_type=abstract
Reports on Progress in Physics (ISSN 0034-4885), vol. 48, July 1985, p. 907-954.
Mathematics
34
Annihilation Reactions, Atomic Energy Levels, Atomic Spectra, Quantum Mechanics, Angular Momentum, Computer Programs, Configuration Interaction, Hartree Approximation, Hyperfine Structure, Least Squares Method, Lie Groups, Matrices (Mathematics), Operators (Mathematics), Orthogonal Functions, Relativistic Effects, Tensors, Transition Probabilities, Trees (Mathematics), Zeeman Effect
Scientific paper
The long history of the theory of complex spectra, as distinct from series spectra, is reviewed from the period of the 1930s, when quantum mechanics was rapidly applied to solve a variety of problems, to the present day, when computer programs are used to fit many hundreds of atomic energy levels to theoretical mdoels. Emphasis is placed on the use of annihilation and creation operators. The role that Lie groups play in atomic spectra can be described in analogy to SO(3), the special orthogonal group corresponding to rotations in ordinary three-dimensional space. Configuration interaction is represented by effective operators that act within the states of the unperturbed configuration under study. These effective operators are also usefully constructed from annihilation and creation operators. A table is given in which the least-squares fit to the levels of atomic configurations comprising at least three electrons (or electron holes and electrons).
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