By D.R. BATES (Eds.)
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We may, however, choose states which are linear combinations of the states with representation (50) and we may do this in such a way that (47) will be satisfied. In order to develop a systematic procedure we require two theorems on commuting operators. 2 Commuting Operators Let A be an operator with eigenvalues a, B an operator with eigenvalues b and let A and B commute: AB — BA = 0. Theorem I states that there exists a set of simultaneous eigenstates φ(αο) of A and B. (Vol. ). Theorem II states that the matrix element (#|£|a') is zero if a is not equal to a'.
Some numerical values are given in Table VI.
Nl, and in which the quantum numbers mUimsi take on all allowed values. For configurations nlu+2n'l' containing one electron outside of closed shells one has S = s = \,L = /', Ms = ms and ML = m\. It may be seen that a single D function may also be used for configurations of this type. * In general it is necessary to employ linear combinations of £)-functions in order to diagonalize the energy matrix within a configuration. 49 1. COMPLEX ATOMS It may be shown in a similar way that single D functions may also be used for configurations nlu+1 in which the number of electrons is one less than the number required to complete a closed shell.
Aggregates of Particles by D.R. BATES (Eds.)