An alternative approach Fock space

Although the Cl method, introduced in Section 3.4 and illustrated in the last section, is in principle extremely simple, requiring nothing more than the use of Slater s rules (p. 63) and enough computing power to solve very large systems of secular equations, it is sometimes useful to adopt a 

Instead of the spin-orbital labels, we could alternatively just give the occupation numbers (0,1) of the whole ordered set of available spin-orbitals for example, 1010010.. . ) would stand for the 2-electron state with electrons in %p2 and %ps, and the corresponding Schrodinger function would be 

When a state vector is represented by a linear combination of such kets, we speak of the occupation-number representation the corresponding vector space, whose basis vectors comprise all possible kets— corresponding to any number of electrons— is called the Fock space. The Fock space thus focuses attention on the state vectors themselves, rather than the wavefunctions that represent them, and extends the space to include state vectors for any number of electrons. This af roach originated in field theory, where the particles are photons that are created or annihilated in emission or absorption processes. The use of Fock space is most commonly described as the method of second quantization . 

To this end, we define operators that connect the different basis vectors in Fock space. We use the standard representation property that if a vector 0 is represented by a function 0(jc) then the vector a P is represented by a0(x), a being any complex number in symbols, 0 0(x) requires ord where A B means with A we 

The order in which the spin-orbitals appear is thus important (as a consequence of the antisymmetry principle), and we adopt the convention that in a ket liy...p) the associated determinant is 

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