Spin küresel harmonikler

Kuantum mekaniğinde, spin küresel harmonikler spinorlar dır ve bu açısal momentum işlemcisinin karesinin özdurumudur, ve böylece vektör küresel harmoniklerin doğal spinoriyel analoğudur .

Bu matris içindeki formu ile verliyor[1]

$Y_{(j-{\frac {1}{2}},{\frac {1}{2}})jm}=\left({\begin{array}{c}{\sqrt {\frac {j+m}{2j}}}Y_{j-{\frac {1}{2}},m-{\frac {1}{2}}}\\{\sqrt {\frac {j-m}{2j}}}Y_{j-{\frac {1}{2}},m+{\frac {1}{2}}}\end{array}}\right)$

$Y_{(j+{\frac {1}{2}},{\frac {1}{2}})jm}=\left({\begin{array}{c}-{\sqrt {\frac {j-m+1}{2j+2}}}Y_{j+{\frac {1}{2}},m-{\frac {1}{2}}}\\{\sqrt {\frac {j+m+1}{2j+2}}}Y_{j+{\frac {1}{2}},m+{\frac {1}{2}}}\end{array}}\right)$

Notlar

Biedenharn, L. C.; Louck, J. D. (1981), Angular momentum in Quantum Physics: Theory and Application, Encyclopedia of Mathematics, 8, Reading: Addison-Wesley, s. 283, ISBN 0-201-13507-8

Kaynakça

Edmonds, A. R. (1957), Angular Momentum in Quantum Mechanics, Princeton University Press, ISBN 978-0-691-07912-7

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[1] Biedenharn, L. C.; Louck, J. D. (1981), Angular momentum in Quantum Physics: Theory and Application, Encyclopedia of Mathematics, 8, Reading: Addison-Wesley, s. 283, ISBN 0-201-13507-8