Calculating the Inner Product of <2011|0011>

[UrbanXrisis]

Homework Statement

What s the inner product &lt;2011|0011&gt;

Homework Equations

C_{m_1m_2}=&lt;l_1l_2m_1m_2|lml_1l_2&gt;

The Attempt at a Solution

I'm not sure how to exactly solve this question. The first thing that came to my mind was the Clebsch-Gordan equation, since that's what it looks like, but then I saw that it doesn't really make any sense because of this:

|lml_1l_2&gt;=|0011&gt;

|l_1l_2m_1m_2&gt;=|2011&gt;

I'm guessing the inner product is zero, but I'm not sure how to show this.

maybe because since m=0, m_1=1 and m_2=1 wouldn't make sense? not too sure, any help would be appreciated.

thanks,
ux

 

[nrqed]

Homework Statement

What s the inner product &lt;2011|0011&gt;

Homework Equations

C_{m_1m_2}=&lt;l_1l_2m_1m_2|lml_1l_2&gt;

The Attempt at a Solution

I'm not sure how to exactly solve this question. The first thing that came to my mind was the Clebsch-Gordan equation, since that's what it looks like, but then I saw that it doesn't really make any sense because of this:

|lml_1l_2&gt;=|0011&gt;

|l_1l_2m_1m_2&gt;=|2011&gt;

I'm guessing the inner product is zero, but I'm not sure how to show this.

maybe because since m=0, m_1=1 and m_2=1 wouldn't make sense? not too sure, any help would be appreciated.

thanks,
ux

Are you sure that your labels are ordered correctly?

Yes, it's a CG question, but here the result is trivially zero. In pricniple, you would have to look up a table and write the state | l_{total} =0, m_{l,total} =0, l_1 =1, l_2=1&gt; in terms of the |l_1,l_2,m_{l,1} m_{l,2}&gt; states.


But if your labels are ordered correctly and l_total = 0 and l_1 = 2 and l_2=0 then the result is trivially zero since adding 2 and 0 only gives a total l equal to 2 (and the m quantum numbers don't match either. if m_1=1 and m_2 =1, then m_total must be 2).

Patrick