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Traces of products of spherical components of angular momentum operators

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Il Nuovo Cimento (1955-1965)

Summary

A method for the generation of distinct products (with nonvanishing traces) of spherical components of angular momentum operators and the evaluation of their traces is presented. As illustrations all possible distinct prototypes of products with up to 4 pairs of raising and lowering operators are constructed and a table with the help of which the traces of these products can be evaluated is given. As examples the traces of a few products of degree 11–15 are evaluated. Relations between traces of certain distinct products are derived and the problem of the construction of tables of traces of degree < 9 is analysed.

Riassitnto

Si espone un metodo per la generazione di prodotti distinti (con tracce che non si annullano) delle componenti sferiche degli operatori del momento angolare e per la valutazione delle loro tracce. Come illustrazione si costruiscono tutti i possibili distinti prototipi di prodotti che hanno sino a 4 coppie di operatori per alzare ed abbassare gli indici e si dà una tabella col cui aiuto si possono calcolare le tracce di questi prodotti. Come esempio si calcolano le tracce di alcuni prodotti di grado 11–15. Si deducono le relazioni fra le tracce di alcuni prodotti distinti e si esamina il problema della costruzione di tabelle delle tracce di grado ≤ 9.

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Authors and Affiliations

  1. Département de Physique, Université de Montréal, Montréal

    A. K. Bose

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  1. A. K. Bose
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Additional information

This work was supported in part by a grant from the National Research Council of Canada, and by the U. S. National Science Foundation.

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Bose, A.K. Traces of products of spherical components of angular momentum operators. Nuovo Cim 38, 385–394 (1965). https://doi.org/10.1007/BF02750466

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  • DOI: https://doi.org/10.1007/BF02750466

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