Foundations of Second Quantization

Explain why first-quantized descriptions are impractical for many identical fermions and motivate the second-quantization formalism.

Define fermionic creation and annihilation operators and verify their canonical anticommutation relations.

Construct normalized N-particle states in Fock space using creation operators and relate them to Slater determinants.

Express a single-particle operator (e.g., kinetic energy) in second-quantized form.

Express a two-particle interaction operator (e.g., Coulomb repulsion) in second-quantized form.

Perform a change of single-particle basis for creation and annihilation operators (e.g., from a real-space to momentum-space basis).