Quantum Chemistry in Fock Space

The many electron-problem of atomic or molecular theory can be formulated either in configuration space (where operators act on the coordinates of the particles) or in Fock space (where operators act on the occupation numbers of spin orbitals). The representation of operators in Fock space (often also referred to as occupation number representation or 2nd quantization) is essentially equivalent to the representation in configuration space, it is, however, more general insofar as a Fock space Hamiltonian has eigenstates with arbitrary numbers of electrons, while in configuration space the number of electrons is fixed. So Fock space is, in a sense, a direct sum of Hilbert spaces for various particle numbers. Processes like ionization or electron attachment, in which the number of electrons is changed are hence better described in Fock space than in configuration space (i.e. in n- particle Hilbert space).