Read e-book online Advances in Quantum Chemistry PDF

By Per-Olov Lowdin

ISBN-10: 0080582338

ISBN-13: 9780080582337

ISBN-10: 012034808X

ISBN-13: 9780120348084

ADVANCES IN QUANTUM CHEMISTRY VOL 8.

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N ) is the exact wavefunction (a solution of the Schrodinger equation) for an N electron system, and that P is any of the N ! permutations of the electrons. Then for any observable operator W , (PY(1,2,. ) N)IWPY(l, 2, .. , N ) ) . Since permutations are unitary operators, it follows that (Y(1,2,. . , N)I P-lWPY(1,2,. , N ) ) = (Y(1, 2, . , N ) I WY(1,2, . . , N ) ) for any wavefunction Y. Thus it must be that W = P-'WP: every observable operator is invariant under similarity transformations that permute its electron labels.

G2‘e= ae g2’e’= ye + pel, + 6e’. The trace of the matrix associated with the element glg2’sis Trace = aci + dS + cp + by. This trace is equal to the character of g1g2 in the representation of the origin x 2 . In that manner we obtain the representation Tsor Tsaccording to the action of s. The representations rl,r2,r3,and r4are obtained in the same way from the representations xl”and xS“. The table of characters thus obtained is identical with that given by Woodman (1966) without details of the construction.

T P .

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Advances in Quantum Chemistry by Per-Olov Lowdin


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