1. The problem statement, all variables and given/known data We just started matrix representation of operators. For the life of me I can't figure out how to construct any of the matrices. For example, the L+ matrix for l=1 (which gives m=-1,0,1). I plug in the 3 values of m into the L+ equation and get sqrt(2), sqrt(2), and 0. Then I have no idea what the next step is to get the matrix.. how do I know where in the matrix to put these values? 2. Relevant equations (It's in the photo.) 3. The attempt at a solution https://docs.google.com/file/d/0B0ByXWZYouOBUTExbmZ4d2lkemM/edit?usp=sharing I have the L+ values for when m=-1, 0, and 1. I just don't know how I'm supposed to know where to put them in a matrix. At the bottom left of the photo, my friend told me that's the next step, to have the -1,0,1 on the top for the rows, and on the left side for the columns, then I put them together like, for example, the first spot would be <-1|L+|-1> but how do I calculate that, what does <-1|L+|-1> mean? I tried plugging in m=-1 and then subtracting/adding and all kinds of experimental stuff but nothing gave me what I wanted. I've spent way too long on this, it's getting frustrating, there must be something obvious that just isn't clicking. I would really, really, really, really appreciate it if someone could help me out. Thanks!