Occupation number representation of quantum states

The occupation number representation provides a compact way of describing systems of identical quantum particles.
📚 In the videos on identical particles we have constructed symmetric and antisymmetric states to describe bosons and fermions. We have written down these states as sums over N! permutations of a given tensor product state, which leads to long expressions. Today we will see that this description has a lot of redundancy built in, and will instead introduce the occupation number representation that provides a much more compact description. Qualitatively, we have so far been describing systems of identical quantum particles by asking the question "which particle is in which state?". In the occupation number representation we instead describe the system by asking the question "how many particles are in each state?". The occupation number representation is a more natural way of describing identical particles, and it forms the basis of second quantization, a powerful formalism that will allow us to study advanced topics like quantum field theory or quantum statistical mechanics.

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⏮️ BACKGROUND
Identical particles: https://youtu.be/1cIl3m-fmnY
Tensor product state spaces: https://youtu.be/kz3206S2B6Q
Permutation operators: https://youtu.be/mgqxywZMTjs
Symmetric and antisymmetric states: https://youtu.be/6pwtOV5mUpo
Exchange degeneracy: https://youtu.be/-HMZNk6VlZ0
Symmetrization postulate: https://youtu.be/hOY51y9iqGQ

⏭️ WHAT NEXT?
Fock space: https://youtu.be/jAw9WMkcCj0
Boson creation and annihilation: https://youtu.be/BhK6u0bMqG0
Fermion creation and annihilation: https://youtu.be/HZ43XE89n8s

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Director and writer: BM
Producer and designer: MC

Видео Occupation number representation of quantum states канала Professor M does Science