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The Wave Equation for Spin 1 in Hamiltonian Form. II
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
Vol. 232, No. 1191 (Nov. 22, 1955), pp. 435-447
Published by: Royal Society
Stable URL: http://www.jstor.org/stable/99821
Page Count: 13
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The investigation is mainly concerned with the relation between constants of the motion and the conservation laws in differential form. The operator that commutes with the Hamiltonian is not the one whose Hermitian form obeys a conservation law and therefore yields, on integration over space, the mean (or expectation) value of the constant. There is a general association between the 'commuting' and the 'conserved' operators; the latter does not in general commute with the Hamiltonian. The duplication stems from normalizing by a non-definite Hermitic form, meaning the charge density. It entails that an elementary wave always carries a positive amount of energy, and a momentum in the direction in which the wave proceeds, though from the eigenvalues of energy and momentum one might expect either sign. A deep-rooted general connexion between charge quantization and the energy aspect of frequency is suggested. An attempt is made to clarify the relation between mechanical and magnetic spin, the latter appearing to depend in a simple way on the fifth Kemmer matrix.
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences © 1955 Royal Society