Find the matrices which represent the following ladder operators a+,a_, and a+a-
All of these operators are supposed to operate on Hilbert space, and be represented by m*n matrices.
a+a_= 1/hw*(H) - 1/2
The Attempt at a Solution
I recognize that once I find the matrix which represents a+, a_ will be represented by the conjugate of the transpose of that matrix. I also can then find a+a_ by matrix multiplication. Not sure about anything else though.