# 4.3. Fermionic creation and annihilation operators

In the previous section, we mentioned that the Fock space is a mathematical construction and does not represent a physical reality nor a chemical actuality. However, please keep in mind that in a molecule, each electron can occupy only one spin-orbit at a time and no two electrons can occupy the same spin-orbit.

Now we further consider a subspace of the Fock space, which is spanned by the **occupation number** of the spin-orbits, which is described by electronic basis states , where is the occupation number of orbital .

The spin-orbital state not occupied by an electron is represented by .

We define a set of fermionic annihilation operators and creation operators , which act on local electron modes, and which satisfy the following **anti-commutation** relations:

where is the Dirac delta function. The operators are called the **occupation number operators** and commute with one...