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| {{Distinguish|Spin-weighted spherical harmonics}}
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| In [[quantum mechanics]], '''spin spherical harmonics''' are [[spinor]]s that are eigenstates of the square of the [[angular momentum operator]], and so are the natural spinorial analog of [[vector spherical harmonics]].
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| They are given in matrix form by<ref>{{Citation | last1=Biedenharn | first1=L. C. | authorlink=Lawrence Biedenharn | last2=Louck | first2=J. D. | title=Angular momentum in Quantum Physics: Theory and Application | publisher=[[Addison-Wesley]] | place=Reading | volume=8 | series=Encyclopedia of Mathematics | isbn=0-201-13507-8 | year=1981 | page=283}}</ref>
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| <math> | |
| Y_{(j-\frac{1}{2},\frac{1}{2})jm}=\left(\begin{array}{c}
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| \sqrt{\frac{j+m}{2j}}Y_{j-\frac{1}{2},m-\frac{1}{2}}\\
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| \sqrt{\frac{j-m}{2j}}Y_{j-\frac{1}{2},m+\frac{1}{2}}\end{array}\right)
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| </math>
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| <math>
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| Y_{(j+\frac{1}{2},\frac{1}{2})jm}=\left(\begin{array}{c}
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| -\sqrt{\frac{j-m+1}{2j+2}}Y_{j+\frac{1}{2},m-\frac{1}{2}}\\
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| \sqrt{\frac{j+m+1}{2j+2}}Y_{j+\frac{1}{2},m+\frac{1}{2}}\end{array}\right)
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| </math>
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| ==Notes==
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| {{Reflist}}
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| ==References==
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| * {{Citation | last1=Edmonds | first1=A. R. | title=Angular Momentum in Quantum Mechanics | publisher=[[Princeton University Press]] | isbn=978-0-691-07912-7 | year=1957}}
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| [[Category:Spinors]]
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| [[Category:Rotational symmetry]]
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| [[Category:Special functions]]
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| {{Physics-stub}}
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Latest revision as of 18:32, 5 December 2014
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