Operators pair creation

That means the pair creation operator A P is expressed linearly in terms of a product of elementary particles operators... 

In addition to the DFT chapters, there are two chapters by John and James Avery the first time a father and son team has published in Advances. In the first, a new and more general type of symmetry-preserving pair creation operator is proposed and extended to cases where orthonormality of orbitals of different configurations cannot be assumed. 

Configuration interaction using Kramers pair creation operators 193... 

More general symmetry-preserving pair creation operators 197... 

In the present paper, we shall discuss a method for generating many-electron states of a given symmetry using Kramers pair creation operators and other symmetry-preserving pair creation and annihilation operators. We will first develop the formalism for the case where orthonormality between the orbitals of different configurations can be assumed. Afterwards we will extend the method to cases where this orthonormality is lost, so that the method also can be used in generalized Sturmian calculations [11-13] and in valence bond calculations. 

Using Kramers concept of time-reversal, it is possible to construct symmetry preserving pair creation operators of the form [5,7,8]... 

As an example of the symmetry-preserving Kramers pair creation operators, we can think of the case of D3 symmetry, where they have the form [8] ... 

Notice that the summation of equation (36) has been simplified. Since each state in the set y appears twice in the sum, coupled with its time-reversed partner, equation (32) can be used to cut the number of terms in half. Strictly speaking, each of the pair creation operators shown in equation (43) ought to have an additional index specifying the particular set of molecular orbitals to which it corresponds. 

As a second example, we can think of the case where the one-electron Hamiltonian has spherical symmetry. Then the Kramers pair creation operator corresponding to the shell n and subshell l is given by... 

Here, just as in equation (43) we have cut the number of terms in the sum in half, since each orbital appears twice in the sum shown in equation (36). In equation (44) we have included the shell index n explicitly in the label of the symmetry-preserving pair creation operator. In the individual one-electron creation operators of equation (44), this index is implied, as is the subshell index /. 

The commutation relations (42) can be used to normalize the A-electron states obtained by acting on (A — 2)-electron states with Kramers pair creation operators [8], Suppose that P) is a properly normalized (N — 2)-electron state which is annihilated by By, i.e., suppose that... 

CONFIGURATION INTERACTION USING KRAMERS PAIR CREATION OPERATORS... 

In other words, when a Kramers pair creation operator acts on an (N — 2)-electron state 1,4). which is an eigenfunction of the core Hamiltonian, it produces an /V-electron state which is also an eigenfunction of //, with an eigenvalue increased... 

From the argument given above, it can also be seen that the Kramers pair creation operators B t commute with S, since w nl = -JlB v... 

Commutation relations analogous to (42) can also be derived for the more general symmetry-preserving pair creation operators ... 

The example discussed above was the case of spherical symmetry. We can ask whether general symmetry-preserving pair creation operators analogous to Ikj, can be constructed for other types of symmetry. For example, does the operator... 

The electron interaction terms are considerably more complicated than the one-electron part. They may be analyzed using the pair creation operators of Eq. (4.149). In Table 10.1 we give them in cartesian form for the limited basis. 

Table 10.1 Pair creation operators for a set of - and p-operators in cartesian form. Other operators for S = 1 can readily be obtained from the ones given using the step-down operator such that [S, 7rt(S, M5)] = S, Ms)[ S -b...

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