Proving the COMMUTATOR relation [S^2,Sz] = 0 = [S^2,Sx] = [S^2,Sy] - [Quantum Mechanics Tutorial]
In this video, I give a step by step proof of the commutator relation [S^2,S_z]=[S^2,S_x]=[S^2,S_x]=0 for the spin operators. The required commutation relations between the spin matrices S_x. S_y and S_z, and the generic properties of the commutators in quantum mechanics have been written, proved and explained as needed. This makes the video self sufficient in all respects.
In the end, I explain an important physical consequence of these commutation relations. I also give a remark on the connection of these with the similar relations for the orbital angular momentum operators.
Hope you guys find it useful!
More tutorials on SPIN: (Playlist) • Spin in Quantum Mechanics - LECTURE SERIES
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I'm Priyanshi Bhasin, a PhD candidate at the Indian Institute of Science (IISc).
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#Commutators #Spin #SpinMatrices #Sz #Sx #Sy #S^2