So the eigenvectors would have to satisfy exp(iπσx/2)v = Av where A is the eigenvalue. I know that eigenvectors of σx are (1,1) and (1,-1)
Thanks for your help.
I've realized that when written as the two sums, it's clear that there are only two linearly independent eigenvectors for each sum. I'm not sure how it works when the i's get multiplied in though. Aren't there infinite eigenvalues to reflect the infinite nature of the sums?
Homework Statement
Find the eigenvectors and eigenvalues of exp(iπσx/2) where σx is the x pauli matrix:
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01
Homework Equations
I know that σxn = σx for odd n
I also know that σxn is for even n:
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I also know that the exponential of a matrix is defined as Σ(1/n!)xn where the sum runs...