A unitary calculus for electronic orbitals - download pdf or read online

By W. G. Harter, C. W. Patterson

ISBN-10: 0387076999

ISBN-13: 9780387076997

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By W. G. Harter, C. W. Patterson

ISBN-10: 0387076999

ISBN-13: 9780387076997

Show description

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43 shows an example of this and further details are given in Appendix A. ~ . This is derived in Appendix A. I/N~ = ~ p~i D ~ (44) (pI) ] ½ It can be shown that the preceeding formulation completely and unambiguously defines the bases for Gelfand representations which have been used in Secs. i-2. ) However, the significance of the 0~) labels on these basis states needs to be clarified. In all cases we find that for each allowed S n tableau ~ w e get another complete basis for a U Gelfand reprem sentation defined by Young frame (~).

The tables exhibit the vk(~l~2) matrices for 4 - 4 =A>o, and the transpose is found using the symmetry relation in Eq. 38. ~o see the implied physical distinction between operators with A=0 on One hand, and those with A~0 on the other, we may compare the two types of vector (k=l) operators which we will be using shortly. The A=O operators vl(pp) or vl(dd) correspond q q to components of the angular momentum operator L or any other q polar vector operators like those of magnetic dipole. The Z = +1 operators V~(pd) or V~(dp) correspond to the electric dipole or any other axial vector operator.

38. ~o see the implied physical distinction between operators with A=0 on One hand, and those with A~0 on the other, we may compare the two types of vector (k=l) operators which we will be using shortly. The A=O operators vl(pp) or vl(dd) correspond q q to components of the angular momentum operator L or any other q polar vector operators like those of magnetic dipole. The Z = +1 operators V~(pd) or V~(dp) correspond to the electric dipole or any other axial vector operator. The former conserves parity while the latter changes it.

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A unitary calculus for electronic orbitals by W. G. Harter, C. W. Patterson


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