Raising and Lowering momentum operators

[soul]

I tried to use the eigenvalue of the operators but I couldn't get the result.
Can anyone help me to understand this relationship?

Thank you.

 

[Sisplat]

if you multiply out the brackets inside the square root, you will find that they are in fact the eigenvalues of the L+ and L- operators.

Remember that L+|l,m2> = Eigenvalue*|l,m2+1>

Once you have operated with L+ on the left hand side you can move the eigenvalue out to the front as it is just a number. You are left with:

<l,m1|l,m2+1>, which, by orthogonality, is 0 unless m1 = m2+1. This is precisely what the dirac delta functions on the right hand side represent.