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On the representations of the rotation group
Author(s) -
Corio P. L.
Publication year - 1972
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560060208
Subject(s) - mathematics , kravchuk polynomials , rotation matrix , rotation (mathematics) , rotation group so , group (periodic table) , pure mathematics , matrix (chemical analysis) , irreducible representation , relation (database) , algebra over a field , recurrence relation , orthogonal polynomials , combinatorics , discrete orthogonal polynomials , quantum mechanics , physics , geometry , wilson polynomials , computer science , chemistry , chromatography , database
The matrices of the irreducible representations of the 3‐dimensional rotation group are shown to be related to Krawtchouk's orthogonal polynomials of a discrete variable x = j – m ', whose degrees are given by n = j + m . The relation follows directly from the recurrence formulas satisfied by the matrix elements and permits a concise development of the formal properties of the rotation matrices. In particular, an asymptotic relation for large j is developed that generalizes a formula first discussed for a special case by Wigner.