Find the eigenvectors and eigenvalues of exp(iπσx/2) where σx is the x pauli matrix:
I know that σxn = σx for odd n
I also know that σxn is for even n:
I also know that the exponential of a matrix is defined as Σ(1/n!)xn where the sum runs from n=0 to infinity
The Attempt at a Solution
Using knowledge of the matrix exponential, I can say that exp(iπσx/2) = Σ(1/n!)(iπσx/2)n. I can then split this into two sums, one for even n and one for odd n. This allows me to take the power off the matrices for easier summing. It's then that I get stuck. I've attached a file showing the two sums because it's easier and clearer to show you this way.[/B]
I'd really appreciate any help that can be given.