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## Homework Statement

Ok, this my not be appropriate topic to post my question but it is related to QM (moderators, feel free to move the thread if needed). I don't have any calculations nor do I have anything interesting to write. I am just trying to learn to read the Clebsch-Gordan coefficients from the tables - but I am having hard time understanding them...

Here is the table http://pdg.lbl.gov/2002/clebrpp.pdf

## Homework Equations

## The Attempt at a Solution

Now using this table above, we wrote $$|\frac 3 2 , \frac 1 2 >=\sqrt{\frac 1 3}|\uparrow >|1>+\sqrt{\frac 2 3}|\downarrow >|0>$$ and $$|\frac 1 2 , \frac 1 2 >=\sqrt{\frac 2 3}|\uparrow >|1>-\sqrt{\frac 1 3}|\downarrow >|0>$$ Is there anybody that has 5 minutes of free time and could give me an idiot proof explanation? How do these tables work?