On the representations of the rotation group | Zendy

Corio P. L. | Zendy

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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.

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