- #1
Decimal
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Hello,
I encountered the following statement in my lecture notes and there is a couple of things I don't understand:"Let's consider two particles with spins ##s_1 = \frac{1}{2}## and ## s_2 = 1## with a spherically symmetric interaction potential. Assume these two particles are in a two particle state with orbital quantum number ##l=2##. Now a measurement of ##L^2## will always give the value ##6 \hbar^2##."
First, I assume this means that the total orbital quantum number of the two particles is equal to 2? If both particles were to carry ##l=2## this would result in a total quantum number ##l_{tot}=4## right? This would mean the measurement of ##L^2## should give ##20\hbar^2##. Again, please correct me if I am wrong.
Also I thought when adding up angular momenta there would always be multiple possible values. So let's say we add up two ##l=2## particles then the total orbital angular momenta would be ##l_{tot} = 4,3,2,1,0##. Then one would also find multiple values for ##L^2## right? Yet apparently there is only one value, so what am I not understanding?
I feel like I am missing something, so any help would be greatly appreciated! Thanks!
I encountered the following statement in my lecture notes and there is a couple of things I don't understand:"Let's consider two particles with spins ##s_1 = \frac{1}{2}## and ## s_2 = 1## with a spherically symmetric interaction potential. Assume these two particles are in a two particle state with orbital quantum number ##l=2##. Now a measurement of ##L^2## will always give the value ##6 \hbar^2##."
First, I assume this means that the total orbital quantum number of the two particles is equal to 2? If both particles were to carry ##l=2## this would result in a total quantum number ##l_{tot}=4## right? This would mean the measurement of ##L^2## should give ##20\hbar^2##. Again, please correct me if I am wrong.
Also I thought when adding up angular momenta there would always be multiple possible values. So let's say we add up two ##l=2## particles then the total orbital angular momenta would be ##l_{tot} = 4,3,2,1,0##. Then one would also find multiple values for ##L^2## right? Yet apparently there is only one value, so what am I not understanding?
I feel like I am missing something, so any help would be greatly appreciated! Thanks!