Ciro Santilli
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# Angular momentum operator

| 🗖 nosplit | ↑ parent "Uncertainty principle" | 217, 226, 1
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Basically the operators are just analogous to the classical ones e.g. the classical: $$Lz​=xpy​−ypx​ (36)$$ becomes: $$L^z​=−iℏ(x∂y∂​−y∂x∂​) (37)$$
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Besides the angular momentum in each direction, we also have the total angular momentum: $$L^2=L^x​+L^y​+L^z​ (38)$$
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Then you have to understand what each one of those does to the each atomic orbital:
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There is an uncertainty principle between the x, y and z angular momentums, we can only measure one of them with certainty at a time. Video 71. ""Quantum Mechanics 7a - Angular Momentum I" by ViaScience (2013)" justifies this intuitively by mentioning that this is analogous to precession: if you try to measure electrons e.g. with the Zeeman effect the precess on the other directions which you end up modifing.
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