 #1
 3
 0
Homework Statement
Find the eigenvectors and eigenvalues of exp(iπσ_{x}/2) where σ_{x} is the x pauli matrix:
10
01
Homework Equations
I know that σ_{x}^{n} = σ_{x} for odd n
I also know that σ_{x}^{n} is for even n:
01
10
I also know that the exponential of a matrix is defined as Σ(1/n!)x^{n} 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(iπσ_{x}/2) = Σ(1/n!)(iπσ_{x}/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.
Attachments

35.9 KB Views: 406