Professor M does Science | One body operators in second quantization @ProfessorMdoesScience | Uploaded October 2020 | 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 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. We show this taking the simplest possible case as an example: one body operators like position or momentum that only act on one particle at a time.

🐦 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
Boson creation and annihilation: youtu.be/BhK6u0bMqG0
Fermion creation and annihilation: youtu.be/HZ43XE89n8s

⏭️ WHAT NEXT?
Two-body operators: youtu.be/vgiSgjmRXuQ
Change of basis: youtu.be/6icXRi5lGWE
Hamiltonian in second quantization: youtu.be/hes8XQAg750

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Director and writer: BM
Producer and designer: MC