matrix elements and the real part of corresponding harmonic functions of cubic operator basis in J = 1 case.
32.
Demanding that the classical equations of motion are preserved is not a strong enough condition to determine the matrix elements.
33.
But " individual " matrix elements are frequently computed, especially for the Lie algebra ( below ).
34.
The inter atomic overlap matrix elements \ alpha _ { m, l } should be rather small or neglectable.
35.
"' Sequencing "'methods try to order the matrix elements such that no feedback marks remain.
36.
Determination of each matrix element requires at least one double integration involving the weighting functions, which may become computationally intensive.
37.
This gives an algebraic relation involving " K " and some or all of the 44 unknown matrix elements.
38.
Since the transition rates are given by the matrix elements of, wherever is zero, the corresponding transition should be absent.
39.
Now, this process will only yield integers for the matrix elements while the real inverse you seek will be rational numbers.
40.
The condition that the K matrix elements add up to one becomes the condition that the R matrix elements add up to zero:
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