- #1

Sekonda

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I'm not exactly sure how much this question wants, however the two in question are parts a) and b) below.

So part a) asks to write the expression for the total angular momentum J, I though this was just:

[tex]\hat{J}=\hat{J}^{(1)}+\hat{J}^{(2)}[/tex]

but when we come to showing it satisfies similar commutation relations - I'm not really sure how to do this, I was thinking of expanding J like so

[tex]\hat{J}=\hat{J}_{x}+\hat{J}_{y}+\hat{J}_{z}=(\hat{J}^{(1)}_{x}+\hat{J}^{(2)}_{x})+(\hat{J}^{(1)}_{y}+\hat{J}^{(2)}_{y})+(\hat{J}^{(1)}_{z}+\hat{J}^{(2)}_{z})[/tex]

but wasn't sure if this was the correct route and if the last expansion or even the first was necessary.

Part b I think relies on the commutation relations which we find in a) - I'm fairly sure I can show that they all commute but I don't know what expansion/what other commutation relation I need to derive in order to show these commutators are conserved.

Thanks for any help!

SK