Effective operators eigenvectors, norms

The o(a l are not unity normed but are normalized according to (2.30) which implies that the a )o must first be evaluated. Hence, Eq. (2.46) provides a somewhat cumbersome expression for in terms of left eigenvectors only. An expression with unity normed left eigenvectors is simpler. Since these vectors are the unity normed right eigenvectors of the latter expression reduces to case 1 (with mappings (L, K ) see remark below Eq. (2.41)). Thus, only expressions (2.42), (2.44) and (2.45) need to be considered. These produce the effective operator definitions A" and A p of Table I, each of which is state dependent, that is, depends on the particular a and through the presence of and N,. 

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