What are L+ and L- matrices for l=3 ?

[niloun]

Hi everyone
I need raising and lowering operators for l=3 (so it should be 7 dimensional ).
is it enough to use this formula:
(J±)|j, m > =sqrt(j(j + 1) - m(m ± 1))|j, m ± 1 >
The main problem is about calculating lx=2 for a given wave function , I know L^2 and Lz but I need L+ and L- to solve the problem.
Thanks in advance

 

[DrClaude]

Hi everyone
I need raising and lowering operators for l=3 (so it should be 7 dimensional ).
is it enough to use this formula:
(J±)|j, m > =sqrt(j(j + 1) - m(m ± 1))|j, m ± 1 >
The main problem is about calculating lx=2 for a given wave function , I know L^2 and Lz but I need L+ and L- to solve the problem.
Thanks in advance

Yes, you can use that formula. Matrix elements for an operator $\hat{A}$ are simply given by
$$
A_{ij} = \langle i | \hat{A} | j \rangle
$$