Transformation relations for the conventional O_k^q and normalised O'_k^q Stevens operator equivalents with k=1 to 6 and -k⩽q⩽k

Extensions of the conventional Stevens operators O_kq to negative values of q and their transformation properties are reviewed and reconsidered. Transformation matrices with k=1 to 6 and -k<or=q<or=+k for a general rotation ( Phi , Theta ) of the frame of coordinates are derived by computer using ALTRAN and the corresponding matrices for the operators T_lm. As a special case a transformation which is particularly useful in EPR studies is considered. In the interest of transcription accuracy, the computer-derived transformation relations are reproduced from camera-ready computer output. The present results for k=3 and 5, all q, and k=6, q=1 and 5, are new. A number of inconsistencies in the earlier papers are pointed out for k=2, 4 and 6. The concept of 'normalised' Stevens operators O'_k^q is extended to k=3 and 5 where numerical coefficients relating both sets of operators are given. The transformation matrices for the normalised Stevens operators can be read in a straightforward way from the expressions for the conventional operators. The conclusion is that both the conventional and normalised Stevens operators do transform consistently contrary to some earlier opinions.