The Principles of Quantum Mechanics by P. A. M. Dirac

Author:P. A. M. Dirac [Dirac, P. A. M.]
Language: eng
Format: epub, pdf
Publisher: Lulu.com
Published: 2014-04-14T16:00:00+00:00

Now each eigenvalue K′ of K will be associated with the eigenvalues K′, K′−ħ, K′−2ħ, . . . , −K′ for Mz, with the same number of independent simultaneous eigenkets of K and Mz for each of them. The total number of independent eigenkets of Mz belonging to any eigenvalue must be the same, whether we take them to be simultaneous eigenkets of m1z and m2z or simultaneous eigenkets of K and Mz, i.e. it is always given by the scheme (46). It follows that the eigenvalues for K are

and that for each of these eigenvalues for K and an eigenvalue for Mz going with it there is just one independent simultaneous eigenket of K and Mz.

The effect of rotations on eigenkets of angular momentum variables should be noted. Take any eigenket of the z component of total angular momentum for any dynamical system, and apply to it a small rotation through an angle δϕ about the z-axis. It will change into

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