Permutation operators in quantum mechanics

How does the permutation of particles work in quantum mechanics?

📚 In this video we learn about permutation operators, which allow us to exchange particles in quantum mechanics. We start with a simple example using balls and boxes to introduce the idea of a permutation, which amounts to a re-ordering of the balls, and the idea of a transposition, which amounts to an exchange of two balls. We then see how these ideas can be used to define permutation operators --the tool that allows us to exchange quantum particles--, and we also have a brief taster of group theory. Projection operators are essential for the mathematical study of systems of identical particles, for example the electrons in atoms, molecules, or materials.

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⏮️ BACKGROUND
Tensor product state spaces:    • Tensor product state spaces  
Operators in quantum mechanics:    • Operators in quantum mechanics  
Adjoint operators:    • Try it yourself: the adjoint operator in q...  
Hermitian operators:    • Hermitian operators in quantum mechanics  

⏭️ WHAT NEXT?
Symmetric and antisymmetric states:    • Symmetric and antisymmetric states of many...  
Exchange degeneracy:    • Is quantum mechanics "broken"? | Exchange ...  
The symmetrization postulate:    • Bosons and fermions: the symmetrization po...  

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Director and writer: BM
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