dorsal/arxiv
View SchemaNew Treatment of Systems of Compounded Angular Momentum
| Authors | Habatwa Vincent Mweene |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9907082 |
| URL | https://arxiv.org/abs/quant-ph/9907082 |
Abstract
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.
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"abstract": "The approach to quantum mechanics which we have used to derive the matrix\ntreatment of spin from first principles is now employed to treat systems of\ncompounded angular momentum. A general treatment is first given, which is then\napplied to the concrete cases of a spin-0 and a spin-1 system obtained by\nadding the spins of two spin-1/2 systems. Thus the probability amplitudes for\nmeasurements on the systems are derived, as well as the matrix vectors and\noperators corresponding to the systems. The matrix operators and states\nobtained are different from the standard forms and are much more generalized.\nThe new results are applied to the case of joint measurements on the subsystems\nof such a system; this is a problem that has been made very topical by the high\nlevel of interest in the foundations of quantum mechanics. As a consequence of\nthe insights arising from this treatment, we show that the Clebsch-Gordan\ncoefficients are amenable to generalization, and we give the generalized forms\nfor these cases.",
"arxiv_id": "quant-ph/9907082",
"authors": [
"Habatwa Vincent Mweene"
],
"categories": [
"quant-ph"
],
"title": "New Treatment of Systems of Compounded Angular Momentum",
"url": "https://arxiv.org/abs/quant-ph/9907082"
},
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