Professor M does Science | Two body operators in second quantization @ProfessorMdoesScience | Uploaded October 2020 | Updated October 2024, 2 hours 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 action of an operator on systems of identical particles should not be affected by the exchange of any two particles. To capture this symmetry in first quantization we have to write these operators using a large number of terms. In this video we learn how to write operators using second quantization, where all the subtleties of particle exchange symmetry are captured by the algebras of creation and annihilation operators, dramatically reducing the number of terms. Building up from the video on one body operators, in this video we look at the important possible case of two body operators like the Coulomb interaction between two charged particles.

🐦 Follow me on Twitter: twitter.com/ProfMScience

⏮️ BACKGROUND
Symmetric and antisymmetric states: youtu.be/6pwtOV5mUpo
Symmetrization postulate: youtu.be/hOY51y9iqGQ
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

⏭️ WHAT NEXT?
Change of basis: youtu.be/6icXRi5lGWE
Hamiltonian in second quantization: youtu.be/hes8XQAg750
Heisenberg picture in second quantization: [COMING SOON]

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Director and writer: BM
Producer and designer: MC