1999/07/26 by Habatwa Vincent Mweene, Mweene, Habatwa Vincent · 2 citations
Engineering · Physics and Astronomy · #Electrohydrodynamics and Fluid Dynamics #FOS: Physical sciences #Quantum Physics (quant-ph) #quant-ph
paper · pdf · doi:10.48550/arxiv.quant-ph/9907082
44 pages, LateX. The notation has been thoroughly revised to improve comprehension and to facilitate further development of the theory. Some typographical errors have been corrected
openalex publication_date 1999/07/26 · arxiv created 2000/03/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The approach to quantum mechanics which we have used to derive the matrix treatment of spin from first principles is now employed to treat systems of compounded angular momentum. A general treatment is first given, which is then applied to the concrete cases of a spin-0 and a spin-1 system obtained by adding the spins of two spin-1/2 systems. Thus the probability amplitudes for measurements on the systems are derived, as well as the matrix vectors and operators corresponding to the systems. The matrix operators and states obtained are different from the standard forms and are much more generalized. The new results are applied to the case of joint measurements on the subsystems of such a system; this is a problem that has been made very topical by the high level of interest in the foundations of quantum mechanics. As a consequence of the insights arising from this treatment, we show that the Clebsch-Gordan coefficients are amenable to generalization, and we give the generalized forms for these cases.