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

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

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Example text

_ . ~J~ ~ -~ . . . . . . . - ................... :~ . ~ :~ -~ '~ ~- I ~Ic~:~l~ -,>. ~---~ : c~ . ~ I . . • I . ,, ~ ... . - :: ~ "~ ~',-i ~- ~ • ~-~ . ~i~i~---~. SSs L~L~I~ ~ ..... ~ ..... ,--i II ~-4 L",I O,l . 25. 26a) and the desired interaction matrix (Eq26b). ,,31T> o -9IT> - (26c) v3. ) to label the repeated states. V ~ are multiples in the ([It , LII> ) representation,(M 1 of the unit matrix is the U s invariant, 1 while V -V is proportional to L 2) so eigenvectors of V3.

Llb. ~ 3 -2/~ of If the result is null, ing columns is found. lJ) = li+2), lj) = Ii~1) just one compo- the routine must try the follow- Ii+3) . . until a non-null A good thing about the routine of calculations ~I II). A simple test routine exists which will check this by calculating nent. 4 result is that the number needed to obtain an orthonormal vector is constant no matter how far the test goes before getting a non-null result. 12b) is non-zero. e. 12a, using the j=m-th column. 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.

For (d) 3doublets 33 ' ,. Then all the U m (m=2~+1) "lowering operators" E21, E32'E43 . . . Em m-1 are applied once to the initial tableau. The new tableaus that result are transcribed along with the matrix elements (Recall Fig. 9) for the change. Only tableaus that have the numbers equal or increasing toward the right in their rows, and increasing but not equal down their columns, are transcribed, For (d) 3 doublets we obtain 11 the tableaus ~2 and 3 =1 a n d < ~ l l with matrix elements -2 <121 E21 211~ / E321 ~1~ =i respectively.

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