# Inner product

UrbanXrisis

## Homework Statement

What s the inner product $$<2011|0011>$$

## Homework Equations

$$C_{m_1m_2}=<l_1l_2m_1m_2|lml_1l_2>$$

## 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 doesnt really make any sense because of this:

$$|lml_1l_2>=|0011>$$

$$|l_1l_2m_1m_2>=|2011>$$

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 wouldnt make sense? not too sure, any help would be appreciated.

thanks,
ux

Homework Helper
Gold Member

## Homework Statement

What s the inner product $$<2011|0011>$$

## Homework Equations

$$C_{m_1m_2}=<l_1l_2m_1m_2|lml_1l_2>$$

## 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 doesnt really make any sense because of this:

$$|lml_1l_2>=|0011>$$

$$|l_1l_2m_1m_2>=|2011>$$

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 wouldnt 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 $| l_{total} =0, m_{l,total} =0, l_1 =1, l_2=1>$ in terms of the $|l_1,l_2,m_{l,1} m_{l,2}>$ 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