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In a textbook, I found this relation for eigenvalues of total angular momentum: $$(L^2)_{mn} = \langle l,m \rvert L^2 \lvert l,n\rangle = \hbar^2l(l+1)\delta_{mn}$$

What is the $\delta_{mn}$ refer to? The book does not explain.

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up vote 12 down vote accepted

It means that only when m and n are equal the value is 1, otherwise it is zero.

Check http://en.wikipedia.org/wiki/Kronecker_delta for more information.

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