The Hamiltonian in second quantization

📝 Problems+solutions:
Second quantization: professorm.learnworlds.com/course/second-quantizat…
Quantum field operators: professorm.learnworlds.com/course/quantum-field-op…

📚 The Hamiltonian is the operator associated with the total energy of a quantum system. It plays a key role in quantum mechanics, as it is the operator that drives the time evolution of quantum systems. When we have a system of identical quantum particles, we work in the second quantization formulation of quantum mechanics. In this video, we write down the Hamiltonian operator of a general quantum system in second quantization.

0:00 Introduction
0:43 Hamiltonian operator
3:54 Hamiltonian in second quantization
9:16 Non-interacting Hamiltonian
13:45 Hamiltonian in non-interacting basis
15:22 Wrap-up

⏮️ BACKGROUND
Occupation number representation:    • Occupation number representation of quantu...  
Fock space:    • Fock space: variable number of quantum par...  
Creation and annihilation of bosons:    • Boson creation and annihilation operators  
Creation and annihilation of fermions:    • Fermion creation and annihilation operators  
One body operators:    • One body operators in second quantization  
Change of basis:    • Changing basis in second quantization  

⏭️ WHAT NEXT?
Heisenberg picture in second quantization: [COMING SOON]
Hamiltonian in terms of field operators: [COMING SOON]

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Director and writer: BM
Producer and designer: