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Many-body physics fundamentals
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Module 1
The Formalism of Second Quantization
1
Fock Space Construction and Manipulation
Construct and manipulate many-body states in the occupation number representation (Fock space).
Bosonic and Fermionic Operators
Define creation/annihilation operators for bosons and fermions and derive their canonical (anti)commutation relations.
Second Quantization: Operators
Express single-particle and two-particle operators in the second-quantized formalism.
Basis Transformations for Operators and States
Transform operators and states between different single-particle bases (e.g., position and momentum).
Normal Ordering for Bosonic and Fermionic Operators
Define normal ordering for bosonic and fermionic operators.
Wick's Theorem and Ground State Expectation Values
State and apply Wick's theorem to evaluate ground state expectation values of operator products.
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