- #1

pstq

- 10

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## Homework Statement

I have to show:

[itex]\sqrt{(j \pm m ) (j \mp m+1} <j_1 j_2 m_1 m_2 | j_1 j_2 j m\mp 1 > = \sqrt{(j_1 \mp m_1 ) (j_1 \pm m_1+1} <j_1 j_2 m_1 \pm1, m_2 | j_1 j_2 j m > +\sqrt{(j_2 \mp m_2 ) (j_2 \pm m_2+1} <j_1 j_2 m_1 , m_2 \pm1 | j_1 j_2 j m > [/itex]

## Homework Equations

Wigner 3-j symbols are related to Clebsch–Gordan coefficients through

[itex]\begin{pmatrix}

j_1 & j_2 & j_3\\

m_1 & m_2 & m_3

\end{pmatrix}

\equiv \frac{(-1)^{j_1-j_2-m_3}}{\sqrt{2j_3+1}} \langle j_1 m_1 j_2 m_2 | j_3 \, {-m_3} \rangle [/itex]

[itex]j_3=j, m_3=m [/itex]

## The Attempt at a Solution

I've tried to put each term [itex] <j_1 j_2 m_1 \pm1, m_2 | j_1 j_2 j m > [/itex] and [itex] <j_1 j_2 m_1 , m_2 \pm1 | j_1 j_2 j m > [/itex] on the matrix form , but I don't know how i can get the square roots, any idea?

thanks in advance