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

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

ISBN-10: 0387076999

ISBN-13: 9780387076997

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Extra info for A unitary calculus for electronic orbitals

Example text

KIi> ... . . Suppose, as before, that the tableaus or components i, j, k .... corresponded to the first non-zero components of II>, II~ , IIII~ .... respectively. °. will require only the i, j, k .... j> in the basis of the equal-M tableaus I ~ , 12> . . In>. (18) ... v _- ... 19b. 47 ~i~> ~II~";

Of the unitary formulation of complex atomic spectra is described i. Here we find one set of formulas and rules that are the same for all configurations~ and no matter how many sub-shells or angular momentum conservation with independent pure or mixed, or electrons We explain a way to take advantage are involved. of rotational symmetry while dealing efficiently terms of equal total orbital momentum and spin multiplicity. oque "lores" of angu- This is done without involving the bar- of the various Racah bases which are necessar- ily quite difficult to teach to a computing machine.

Test for j For each failure we find that j-th component zero, as are all components according preceeding of of the III) is identically the first non-null result. llb. l~ using the k-th column, iIII) is and again the nullity test or norm of also its k-th component. llII) = Ik) ll)(Ilk) - IIl)(IIlk) (Ill) (IIIII) (IIIIIII) = (klk) - (klI) z - ( k I I I ) 2 (IjI) (IIIII) (14a) = (klIII) (14b) 45 Always the result of a nullity test (14b) becomes the k-th component of the new vector. 14b is used again with k~ k+l to get the next (k+l-th) component.

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


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