Sister Celine's polynomials in the quantum theory of angular momentum

• URL: http://arxiv.org/abs/2403.19045v1
• Date: Wed, 27 Mar 2024 22:38:38 GMT
• Title: Sister Celine's polynomials in the quantum theory of angular momentum
• Authors: Jean-Christophe Pain,
• Abstract summary: Jacobi and Hahns are of particular interest for the quantum theory of momentum. In this note, we show that characters of irreducible rotation as well as angular "d" matrices can be expressed as "d" Such connections could lead to new identities for important quantities in quantum mechanics and atomic physics.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The polynomials introduced by Sister Celine cover different usual orthogonal polynomials as special cases. Among them, the Jacobi and discrete Hahn polynomials are of particular interest for the quantum theory of angular momentum. In this note, we show that characters of irreducible representations of the rotation group as well as Wigner rotation "d" matrices, can be expressed as Sister Celine's polynomials. Since many relations were proposed for the latter polynomials, such connections could lead to new identities for quantities important in quantum mechanics and atomic physics.

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