Hermitean conjugate

Similarly, we define the hermitean conjugate operator, ck, as an annihilation operator, which produces a wave function with a fermion missing from the fcth state, if it was occupied, or zero, if not. Thus, in this case, we have... 

A valuable concept in matrix algebra is the hermitean conjugate of a matrix If A is an n x m matrix, then A1 is an m x n matrix with elements... 

Finally, we define an important concept hermitean conjugation of an operator. To every operator A there is a hermitean conjugate A, with the property... 

An important note concerning the phase choice follows. One of the conventions, the standard phase system introduced by Fano and Racah, states that on hermitean conjugation the following property holds true... 

Expressed in this way, the dipole moment operator is the sum of two operators, the first of which is the Hermitean conjugate of the other ... 

Note that the translation operator A(a, a) is unitary, that is, its inverse is equal to its Hermitean conjugate ... 

Where he stands for Hermitean conjugate . The expression of the densit operator pe of the bath is given by Eq. (1.2) and that of the density operator p of the H-bond bridge is... 

Next, consider the Hermitean dipole moment operator [pDim(0)] of the dimer at initial time t = 0, we met in Section VI. A.3. It may be split into two Hermitean conjugate parts, the first one corresponding to absorption and the last one to emission, that is,... 

Then, according to Eq. (Q. 16), the Hermitean conjugate of the u transition moment is... 

The matrices and vectors of this formalism refer to the basis which is formed by the operators Eqs, (14) and (15) together with their deexcitation (hermitean conjugate) counterparts,... 

The first term represents a process in which an electron of spin a is taken out of the f shell and placed in a conduction band state, the Hermitean conjugate represents the... 

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