Banner: Total Angular Momentum Vector
Noun Definition
Total Angular Momentum Vector $\begin{align} &\ \ \ \ \ \ \ \ \ \ \ \ {\rm{\overline{J}}} \equiv \left( {\rm{J}}_{m} , \ {\rm{J}}_{e} , \ {\rm{J}}_{z} \right) \ \ \ \ \ \ \sf{\text{where}} \\ \ \\ \ \\ {\rm{J}}_{m} &\equiv \delta _{\hat{m}} \frac{h}{\mathrm{16} \pi} \sqrt{ \left( N^{\mathsf{A}}-N^{\mathsf{M}} \right)^{2} + 8 \, {\large{\mid}} N^{\mathsf{A}}-N^{\mathsf{M}} {\large{\mid}} \; } \\ \ \\ \ \\ {\rm{J}}_{e} &\equiv \delta _{\hat{e}} \frac{h}{\mathrm{16} \pi} \sqrt{ \left( N^{\mathsf{G}}-N^{\mathsf{E}} \right)^{2} + 8 \, {\large{\mid}} N^{\mathsf{G}}-N^{\mathsf{E}} {\large{\mid}} \; } \\ \ \\ \ \\ {\rm{J}}_{z} &\equiv \delta _{z} \frac{h}{\mathrm{16} \pi} \sqrt{ \left( N^{\mathsf{U}}-N^{\mathsf{D}} \right)^{2} + 8 \, {\large{\mid}} N^{\mathsf{U}}-N^{\mathsf{D}} {\large{\mid}} \; } \end{align}$ 5-40
Unless otherwise stated, the content of this page is licensed under Creative Commons Attribution-ShareAlike 3.0 License