Second Quantization

1. Fock states are constructed via (anti)symmetrizing and normalizing product states. They only depend on occupation numbers and are orthonormal.
2. Creation and annihilation operators couple Fock states with different total occupation numbers. The number operator can be constructed from them.
3. Under the Fock basis, a generic operator can be expressed in terms of creation and annihilation operators. This is known as the “second quantized form” of operators.
4. Properties of Fock states are often related to properties of permutations.

LaTeX Note

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