Group theory or no group theory: understanding selection rules in atomic spectroscopy

[摘要] In the late 1920’s and early 1930’s, physicists applied group representation theory to the quantum mechanics of atomic spectra.At the same time, physicists developed an alternative approach to theoretical atomic spectra that avoids using group theory.These two approaches exhibit nontrivial intellectual differences: the group theoretic approach provides a deeper understanding of many phenomena in atomic spectra.By focusing on derivations of selection rules for atomic spectra, I explicate one case where group theory enhances understanding.I refer to the non-group theoretic approach as the commutator approach; it serves as a benchmark for comparison. This case study motivates a deflationary account of mathematical explanations in science.According to my account, both group theoretic and commutator derivations explain selection rules for atomic spectra.I use these derivations to problematize stronger accounts of mathematical explanation that rely on a notion of relevance.Arguing that selection rules are an example of universality, I also criticize a strong interpretation of Batterman and Rice’s minimal model account of explanations of universality.After examining these accounts of explanation, I argue that explanatory criteria do not distinguish the intellectual content of the group theoretic and commutator approaches.Instead, I develop an account of scientific understanding that distinguishes these approaches based on organizational differences.Adopting terminology from Manders, I argue that these organizational differences arise from differences in the approach’s expressive means.Group theory reorganizes selection rule derivations by re-expressing physical concepts more effectively than the commutator approach.I argue that this superior organizational structure accounts for how group theory provides a heightened understanding of selection rules.

[发布机构] the University of Pittsburgh