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Inner product

  • #1
1,197
1

Homework Statement



What s the inner product [tex]<2011|0011>[/tex]

Homework Equations



[tex]C_{m_1m_2}=<l_1l_2m_1m_2|lml_1l_2>[/tex]

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:

[tex]|lml_1l_2>=|0011>[/tex]

[tex]|l_1l_2m_1m_2>=|2011>[/tex]

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
 

Answers and Replies

  • #2
nrqed
Science Advisor
Homework Helper
Gold Member
3,605
205

Homework Statement



What s the inner product [tex]<2011|0011>[/tex]

Homework Equations



[tex]C_{m_1m_2}=<l_1l_2m_1m_2|lml_1l_2>[/tex]

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:

[tex]|lml_1l_2>=|0011>[/tex]

[tex]|l_1l_2m_1m_2>=|2011>[/tex]

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 [itex] | l_{total} =0, m_{l,total} =0, l_1 =1, l_2=1> [/itex] in terms of the [itex] |l_1,l_2,m_{l,1} m_{l,2}>[/itex] 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
 

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