The discrete Chebyshev–Meckler–Mermin–Schwarz polynomials and spin algebra
The polynomials discovered by Chebyshev and subsequently related to spin transition probabilities by Meckler [Meckler, Phys. Rev. 111, 1447 (1958)] and Mermin and Schwarz [Found. Phys. 12, 101 (1982)] are studied, and their application to phase space representations of spin states and operators is e...
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| Veröffentlicht in: | Journal of mathematical physics 2022-07, Vol.63 (7), p.72101 |
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| description | The polynomials discovered by Chebyshev and subsequently related to spin transition probabilities by Meckler [Meckler, Phys. Rev. 111, 1447 (1958)] and Mermin and Schwarz [Found. Phys. 12, 101 (1982)] are studied, and their application to phase space representations of spin states and operators is examined. In particular, a formula relating the end-point value of the polynomials to scale factors relating different phase space representations of spherical harmonic operators is found. This formula is applied to illustrative calculations of Wigner functions for a single spin and the singlet state of a pair of spins. |
| doi_str_mv | 10.1063/5.0094575 |
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| ispartof | Journal of mathematical physics, 2022-07, Vol.63 (7), p.72101 |
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| source | AIP Journals Complete; Alma/SFX Local Collection |
| subjects | Chebyshev approximation Mathematical analysis Operators (mathematics) Physics Polynomials Representations Spherical harmonics Spin transition Transition probabilities |
| title | The discrete Chebyshev–Meckler–Mermin–Schwarz polynomials and spin algebra |
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