Symmetric and antisymmetric states of many quantum particles

Symmetric and antisymmetric states describe quantum systems of identical particles.

📚 In this video we define totally symmetric and totally antisymmetric states. Totally symmetric states stay the same when we exchange any two particles, while totally antisymmetric states get an extra minus sign when we exchange any two particles. Their properties make them the only quantum states that can describe systems of identical particles. We will also learn how to build these states, using the so-called symmetrizer and antisymmetrizer operators. Finally, we will define totally symmetric operators, that do not change under the exchange of particles. All these ideas will allow us to study the quantum mechanics of systems of identical particles.

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⏮️ BACKGROUND
Identical particles:    • Identical particles in quantum mechanics  
Tensor product state spaces:    • Tensor product state spaces  
Permutation operators:    • Permutation operators in quantum mechanics  
Projection operators:    • Projection operators in quantum mechanics  

⏭️ WHAT NEXT?
Exchange degeneracy:    • Is quantum mechanics "broken"? | Exchange ...  
Symmetrization postulate:    • Bosons and fermions: the symmetrization po...  

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Director and writer: BM
Producer and designer: MC