We derive the orbital angular momentum commutator rules of quantum mechanics. We then establish a connection with the Pauli spin matrices and arrive at the concept of intrinsic spin. Notes downloadable at www.mjtruiz.com
The structure of quantum mechanical angular momentum is treated by working out the algebraic structure of total angular momentum and the z-component. The total angular momentum operator expressed in terms of raising and lowering operators then can be used to work out the ladder of eigenvalues. (This lecture is part of a series for a course based on Griffiths' Introduction to Quantum Mechanics. The Full playlist is at http://www.youtube.com/playlist?list=PL65jGfVh1ilueHVVsuCxNXoxrLI3OZAPI.)
Derivation of the commutator for the 3D quantum mechanical angular momentum operators Lx and Ly - [Lx, Ly].
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Derivation of the Commutator of the 1-D linear position and linear momentum operators.