Professor M does Science | The Hamiltonian in second quantization @ProfessorMdoesScience | Uploaded April 2024 | Updated October 2024, 1 hour ago.
📝 Problems+solutions:
- Second quantization: professorm.learnworlds.com/course/second-quantization
- Quantum field operators: [COMING SOON]

💻 Book a 1:1 session: docs.google.com/forms/d/e/1FAIpQLScUL187erItvC7GPnNU2pelsueyVFr94nRq2A5Eq2aVRdGiIQ/viewform?pli=1

📚 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: youtu.be/hTaqxOK8nGQ
Fock space: youtu.be/jAw9WMkcCj0
Creation and annihilation of bosons: youtu.be/BhK6u0bMqG0
Creation and annihilation of fermions: youtu.be/HZ43XE89n8s
One body operators: youtu.be/8sXWslDlZU0
Change of basis: youtu.be/6icXRi5lGWE

⏭️ 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: MC