Recurrence and Differential Relations for Spherical Spinors |
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Authors: | Radosław Szmytkowski |
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Institution: | (1) Atomic Physics Division, Department of Atomic Physics and Luminescence, Faculty of Applied Physics and Mathematics, Gdańsk University of Technology, Narutowicza 11/12, PL 80–952 Gdańsk, Poland |
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Abstract: | We present a comprehensive table of recurrence and differential relations obeyed by spin one-half spherical spinors (spinor
spherical harmonics) Ωκ μ(n) used in relativistic atomic, molecular, and solid state physics, as well as in relativistic quantum chemistry. First, we
list finite expansions in the spherical spinor basis of the expressions A·B Ωκμ(n) and A·(B×C) Ωκμ(n), where A, B, and C are either of the following vectors or vector operators: n=r/r (the radial unit vector), e
0, e
±1 (the spherical, or cyclic, versors), (the 2×2 Pauli matrix vector), (the dimensionless orbital angular momentum operator; I is the 2×2 unit matrix), (the dimensionless total angular momentum operator). Then, we list finite expansions in the spherical spinor basis of the
expressions A·B F(r)Ωκμ(n) and A·(B×C) F(r)Ωκμ(n), where at least one of the objects A, B, C is the nabla operator , while the remaining ones are chosen from the set . |
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Keywords: | spherical spinors spinor spherical harmonics angular momentum recurrence relations differential relations |
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