Abstract
Basic elements in the theory of angular momentum are the Clebsch—Gordan coefficients for coupling two states characterized by j 1,m 1 and j 2,m 2 into a new state with quantum numbers J,M. The numbers j and their projections, or magnetic quantum numbers1, m have integer or half-odd integer values. Hence, in an exponent to (−1) the quantum numbers must combine to integers as in j ± m or j 1+j 2+J, for example.The notation used for the corresponding Clebsch—Gordan coefficient is (j 1 m 1 j 2 m 2| JM) and it can be non-zero only if j 1, j 2, J fulfil the triangle condition Δ{j 1,j 2,J} equivalent to the condition j 1 + j 2 ≥ J ≥ |j 1 − j 2| and, furthermore, provided that m 1 + m 2 = M. The Clebsch—Gordan coefficients are chosen to be purely real and constitute a unitary transformation.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
