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arXiv:quant-ph/0503061

The Description of Polarization

Habatwa Vincent Mweene

Published Mar 5, 2005• 0 citations
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Abstract

In this paper, we extend to polarization the method we have recently employed to treat spin. We are led to a generalization of its treatment. Thus, we are able to connect its matrix treatment to first principles, and we obtain the most generalized probability amplitudes and operators for its description.
DOI
10.48550/arxiv.quant-ph/0503061

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In a recent paper, we introduced a new way of treating systems of compounded angular momentum. We obtained the probability amplitudes for measurements on the systems and used these to derive the matrix treatment of compounded spin. However, the matrix forms are in 3- and 4- dimensional space and are therefore entirely different from the standard forms. This raises the question of the connection between these forms and the standard forms. In this paper, we answer this question. We not only derive the standard matrix treatment of spin addition - we discover a more generalized form of the theory. We apply the new generalized theory to the singlet and triplet states arising from the addition of the spins of two systems of spin 1/2 each. We obtain new generalized forms of the vectors and operators for these cases, and show that they reduce to the standard forms in the appropriate limit.